Search NASA⌕ Search

SEARCH · Search NASA

Results for “Muscle Development”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Finite Element Modeling Used to Study Stress Distribution on the Foot

A method to study the stress distribution inside the forefoot during walking was developed at the Cleveland Clinic Foundation by a researcher from the NASA Glenn Research Center. In this method, a semiautomated process was outlined to create a three-dimensional, patient-specific, finite element model (FEM) of the forefoot using magnetic resonance images (MRI). The images were processed in Matlab using the k-nearest neighbor (k-NN) classification algorithm and Sobel edge detection to separate the different tissue types: bone, skin, fat, and muscle. This information was used to create curves and surfaces that were exported to an FEM preprocessor known as Truegrid. In Truegrid, eight-noded or brick elements were created by using surface mapping. The FEM was processed and postprocessed in Abaqus. Material properties of the models were obtained from past experiments such as fat pad confined compression, skin axial and biaxial tests, muscle in vivo compressive tests, and reference literature (bone properties). Nonlinear (hyperelastic) material models were used for the skin (epidermis and dermis), fat, and muscles; and a linear elastic model was used for the bones. Muscle activation during walking yielded uncertainties in the muscle material model since contracted muscles are stiffer than relaxed muscles. These uncertainties were resolved by performing a sensitivity analysis of the muscle material properties. The original properties were multiplied by arbitrary factors of 2, 3, 0.5, and 0.33. The strain and stress distributions, as well as the locations of peak values, were similar in all cases. The peak contact pressure P obtained for each case varied with respect to the applied factor f as follows:

Morales, Nelson↗
NASA NTRS1999

Vestibular autonomic regulation (including motion sickness and the mechanism of vomiting)

Autonomic manifestations of vestibular dysfunction and motion sickness are well established in the clinical literature. Recent studies of 'vestibular autonomic regulation' have focused predominantly on autonomic responses to stimulation of the vestibular sense organs in the inner ear. These studies have shown that autonomic responses to vestibular stimulation are regionally selective and have defined a 'vestibulosympathetic reflex' in animal experiments. Outside the realm of experimental preparations, however, the importance of vestibular inputs in autonomic regulation is unclear because controls for secondary factors, such as affective/emotional responses and cardiovascular responses elicited by muscle contraction and regional blood pooling, have been inadequate. Anatomic and physiologic evidence of an extensive convergence of vestibular and autonomic information in the brainstem suggests though that there may be an integrated representation of gravitoinertial acceleration from vestibular, somatic, and visceral receptors for somatic and visceral motor control. In the case of vestibular dysfunction or motion sickness, the unpleasant visceral manifestations (e.g. epigastric discomfort, nausea or vomiting) may contribute to conditioned situational avoidance and the development of agoraphobia.

Review, Tutorial↗
NASA NTRS1998

Current concepts in the pathophysiology, evaluation, and diagnosis of compartment syndrome

This article reviews present knowledge of the pathophysiology and diagnosis of acute compartment syndromes. Recent results using compression of legs in normal volunteers provide objective data concerning local pressure thresholds for neuromuscular dysfunction in the anterior compartment. Results with this model indicate that a progression of neuromuscular deficits occurs when IMP increases to within 35 to 40 mm Hg of diastolic blood pressure. These findings provide useful information on the diagnosis and compression thresholds for acute compartment syndromes. Time factors are also important, however, and usually are incompletely known in most cases of acute compartment syndrome. Although the slit catheter is a very good technique for monitoring IMP during rest, these catheters and their associated extracorporeal transducer systems are not ideal. Recently developed miniature transducer-tipped catheters and, perhaps, future development of noninvasive techniques may provide accurate recordings of IMP in patients with acute compartment syndromes.

NASA Discipline Cardiopulmonary↗
NASA NTRS2015

Human Research Program Advanced Exercise Concepts (AEC) Overview

Exercise countermeasures provide benefits that are crucial for successful human spaceflight, to mitigate the spaceflight physiological deconditioning which occurs during exposure to microgravity. The NASA Human Research Program (HRP) within the Human Exploration and Operations Mission Directorate (HEOMD) is managing next generation Advanced Exercise Concepts (AEC) requirements development and candidate technology maturation to Technology Readiness Level (TRL) 7 (ground prototyping and flight demonstration) for all exploration mission profiles from Multi Purpose Crew Vehicle (MPCV) Exploration Missions (up to 21 day duration) to Mars Transit (up to 1000 day duration) missions. These validated and optimized exercise countermeasures systems will be provided to the ISS Program and MPCV Program for subsequent flight development and operations. The International Space Station (ISS) currently has three major pieces of operational exercise countermeasures hardware: the Advanced Resistive Exercise Device (ARED), the second-generation (T2) treadmill, and the cycle ergometer with vibration isolation system (CEVIS). This suite of exercise countermeasures hardware serves as a benchmark and is a vast improvement over previous generations of countermeasures hardware, providing both aerobic and resistive exercise for the crew. However, vehicle and resource constraints for future exploration missions beyond low Earth orbit will require that the exercise countermeasures hardware mass, volume, and power be minimized, while preserving the current ISS capabilities or even enhancing these exercise capabilities directed at mission specific physiological functional performance and medical standards requirements. Further, mission-specific considerations such as preservation of sensorimotor function, autonomous and adaptable operation, integration with medical data systems, rehabilitation, and in-flight monitoring and feedback are being developed for integration with the exercise countermeasures systems. Numerous technologies have been considered and evaluated against HRP-approved functional device requirements for these extreme mission profiles, and include wearable sensors, exoskeletons, flywheel, pneumatic, and closed-loop microprocessor controlled motor driven systems. Each technology has unique advantages and disadvantages. The Advanced Exercise Concepts project oversees development of candidate next generation exercise countermeasures hardware, performs trade studies of current and state of the art exercise technologies, manages and supports candidate systems physiological evaluations with human test subjects on the ground, in flight analogs and flight. The near term goal is evaluation of candidate systems in flight, culminating in an integrated candidate next generation exercise countermeasures suite on the ISS which coalesces research findings from HRP disciplines in the areas of exercise performance for muscle, bone, cardiovascular, sensorimotor, behavioral health, and nutrition for optimal benefit to the crew.

Countermeasures↗
NASA NTRS1994

Muscular activity and its relationship to biomechanics and human performance

The purpose of this manuscript is to address the issue of muscular activity, human motion, fitness, and exercise. Human activity is reviewed from the historical perspective as well as from the basics of muscular contraction, nervous system controls, mechanics, and biomechanical considerations. In addition, attention has been given to some of the principles involved in developing muscular adaptations through strength development. Brief descriptions and findings from a few studies are included. These experiments were conducted in order to investigate muscular adaptation to various exercise regimens. Different theories of strength development were studied and correlated to daily human movements. All measurement tools used represent state of the art exercise equipment and movement analysis. The information presented here is only a small attempt to understand the effects of exercise and conditioning on Earth with the objective of leading to greater knowledge concerning human responses during spaceflight. What makes life from nonliving objects is movement which is generated and controlled by biochemical substances. In mammals. the controlled activators are skeletal muscles and this muscular action is an integral process composed of mechanical, chemical, and neurological processes resulting in voluntary and involuntary motions. The scope of this discussion is limited to voluntary motion.

Ariel, Gideon↗
NASA NTRS2014

Ames Life Science Data Archive: Translational Rodent Research at Ames

The Life Science Data Archive (LSDA) office at Ames is responsible for collecting, curating, distributing and maintaining information pertaining to animal and plant experiments conducted in low earth orbit aboard various space vehicles from 1965 to present. The LSDA will soon be archiving data and tissues samples collected on the next generation of commercial vehicles; e.g., SpaceX & Cygnus Commercial Cargo Craft. To date over 375 rodent flight experiments with translational application have been archived by the Ames LSDA office. This knowledge base of fundamental research can be used to understand mechanisms that affect higher organisms in microgravity and help define additional research whose results could lead the way to closing gaps identified by the Human Research Program (HRP). This poster will highlight Ames contribution to the existing knowledge base and how the LSDA can be a resource to help answer the questions surrounding human health in long duration space exploration. In addition, it will illustrate how this body of knowledge was utilized to further our understanding of how space flight affects the human system and the ability to develop countermeasures that negate the deleterious effects of space flight. The Ames Life Sciences Data Archive (ALSDA) includes current descriptions of over 700 experiments conducted aboard the Shuttle, International Space Station (ISS), NASA/MIR, Bion/Cosmos, Gemini, Biosatellites, Apollo, Skylab, Russian Foton, and ground bed rest studies. Research areas cover Behavior and Performance, Bone and Calcium Physiology, Cardiovascular Physiology, Cell and Molecular Biology, Chronobiology, Developmental Biology, Endocrinology, Environmental Monitoring, Gastrointestinal Physiology, Hematology, Immunology, Life Support System, Metabolism and Nutrition, Microbiology, Muscle Physiology, Neurophysiology, Pharmacology, Plant Biology, Pulmonary Physiology, Radiation Biology, Renal, Fluid and Electrolyte Physiology, and Toxicology. These experiment descriptions and data can be accessed online via the public LSDA website (http://lsda.jsc.nasa.gov) and information can be requested via the Data Request form at http://lsda.jsc.nasa.gov/common/dataRequest/dataRequest.aspx or by contacting the ALSDA Office at: Alison.J.French@nasa.gov

Life Sciences↗
NASA NTRS1990

Biofeedback for Better Vision

Biofeedtrac, Inc.'s Accommotrac Vision Trainer, invented by Dr. Joseph Trachtman, is based on vision research performed by Ames Research Center and a special optometer developed for the Ames program by Stanford Research Institute. In the United States, about 150 million people are myopes (nearsighted), who tend to overfocus when they look at distant objects causing blurry distant vision, or hyperopes (farsighted), whose vision blurs when they look at close objects because they tend to underfocus. The Accommotrac system is an optical/electronic system used by a doctor as an aid in teaching a patient how to contract and relax the ciliary body, the focusing muscle. The key is biofeedback, wherein the patient learns to control a bodily process or function he is not normally aware of. Trachtman claims a 90 percent success rate for correcting, improving or stopping focusing problems. The Vision Trainer has also proved effective in treating other eye problems such as eye oscillation, cross eyes, and lazy eye and in professional sports to improve athletes' peripheral vision and reaction time.

Source record↗
NASA NTRS1986

Ames Research Center Life Sciences Payload - Overview of results of a spaceflight of 24 rats and 2 monkeys

A hardware description and experimental results are reported from the initial STS flight carrying two Research Animal Holding Facility (RAHF) units. The flight was mainly intended for engineering check-out of the RAHF design. The system development and prelaunch preparations are briefly summarized, including the provisions of retrieval teams at alternate landing sites and extensive rehearsals to ensure timely data analysis. The flight revealed a problem with the containment of particulates from the RAHFs and the provision of adequate water for the monkeys. On-board films showed that one of the monkeys experienced motion sickness, from which he recovered after 5 days in space. Necropsy of the subject rats documented suppressed interferon production, loss of muscle mass, an up to 13 percent loss in bone mass (after a one week flight), and a 20 percent decrease in growth-inducing hormone. The volume of data collected is thought to exceed the combined data gathered on all previous U.S. space missions.

Callahan, P. X.↗
NASA NTRS1997

Applying Space Technology to Enhance Control of an Artificial Arm

At the present time, myoelectric prostheses perform only one function of the hand: open and close with the thumb, index and middle finger coming together to grasp various shaped objects. To better understand the limitations of the current single-function prostheses and the needs of the individuals who use them, The Institute for Rehabilitation and Research (TIRR), sponsored by the National Institutes of Health (August 1992 - November 1994), surveyed approximately 2500 individuals with upper limb loss. When asked to identify specific features of their current electric prosthesis that needed improvement, the survey respondents overwhelmingly identified the lack of wrist and finger movement as well as poor control capability. Simply building a mechanism with individual finger and wrist motion is not enough. Individuals with upper limb loss tend to reject prostheses that require continuous visual monitoring and concentration to control. Robotics researchers at NASA's Johnson Space Center (JSC) and Rice University have made substantial progress in myoelectric teleoperation. A myoelectric teleoperation system translates signals generated by an able-bodied robot operator's muscles during hand motions into commands that drive a robot's hand through identical motions. Farry's early work in myoelectric teleoperation used variations over time in the myoelectric spectrum as inputs to neural networks to discriminate grasp types and thumb motions. The resulting schemes yielded up to 93% correct classification on thumb motions. More recently, Fernandez achieved 100% correct non-realtime classification of thumb abduction, extension, and flexion on the same myoelectric data. Fernandez used genetic programming to develop functions that discriminate between thumb motions using myoelectric signal parameters. Genetic programming (GP) is an evolutionary programming method where the computer can modify the discriminating functions' form to improve its performance, not just adjust numerical coefficients or weights. Although the function development may require much computational time and many training cases, the resulting discrimination functions can run in realtime on modest computers. These results suggest that myoelectric signals might be a feasible teleoperation medium, allowing an operator to use his or her own hand and arm as a master to intuitively control an anthropomorphic robot in a remote location such as outer space.

Atkins, Diane↗
NASA NTRS2005

By Different Cellular Mechanisms, Lymphatic Vessels Sprout by Endothelial Cell Recruitment Whereas Blood Vessels Grow by Vascular Expansion

The development of effective vascular therapies requires the understanding of all modes of vessel formation contributing to vasculogenesis, angiogenesis (here termed hemangiogenesis) and lymphangiogenesis. We show that lymphangiogenesis proceeds by blind-ended vessel sprouting via recruitment of isolated endothelial progenitor cells to the tips of growing vessels, whereas hemangiogenesis occurs by non-sprouting vessel expansion from the capillary network, during middevelopment in the quail chorioallantoic membrane (CAM). Blood vessels expanded out of capillaries that displayed transient expression of alpha smooth muscle actin (alphaSMA), accompanied by mural recruitment of migratory progenitor cells expressing SMA. Lymphatics and blood vessels were identified by confocal/fluorescence microscopy of vascular endothelial growth factor (VEGF) receptors VEGFR-1 and VEGFR-2, alphaSMA (expressed on CAM blood vessels but not on lymphatics), homeobox transcription factor Prox-1 (specific to CAM lymphatic endothelium), and the quail hematopoetic/vascular marker, QH-1. Expression of VEGFR-1 was highly restricted to blood vessels (primarily capillaries). VEGFR-2 was expressed intensely in isolated hematopoietic cells, lymphatic vessels and moderately in blood vessels. Prox-1 was absent from endothelial progenitor cells prior to lymphatic recruitment. Although vascular endothelial growth factor-165 (VEGF(sub 165)) is a key regulator of numerous cellular processes in hemangiogenesis and vasculogenesis, the role of VEGF(sub 165) in lymphangiogenesis is less clear. Exogenous VEGF(sub 165) increased blood vessel density without changing endogenous modes of vascular/lymphatic vessel formation or marker expression patterns. However, VEGF(sub 165) did increase the frequency of blood vascular anastomoses and strongly induced the antimaturational dissociation of lymphatics from blood vessels, with frequent formation of homogeneous lymphatic networks.

Parsons-Wingerter, Patricia↗
NASA NTRS2019

Investigating Neuro-Consequences of Spaceflight Using Drosophila Melanogaster

Research on human acclimation to spaceflight, including the recent NASA's Twin Study, reports complex effects of the spaceflight environment on health, with both acute and prolonged changes in multiple tissues. Spaceflight includes multiple factors such as microgravity, ionizing radiation, physiological stress, and disrupted circadian rhythms, that have been shown to contribute to pathophysiological responses that target immunity, bone and muscle integrity, cardiovascular and nervous systems. In this study, we used a well-established spaceflight model organism, Drosophila melanogaster, to assess spaceflight-associated changes on the nervous system. With 75% disease gene orthology to humans, short generation time, large sample size and ease of genetic, neuronal and behavioral studies, Drosophila is an excellent model to study nervous system dysfunction. Here, we present results from MVP-Fly-01 spaceflight mission that was launched on SpaceX CRS-14. The MVP hardware (developed by Techshot) used in this mission enabled us to have an in-flight 1g centrifuge, to distinguish the changes resulting from gravity versus those induced by other environmental factors associated with spaceflight. We observe behavioral impairments (p<0.001) and synaptic deficits, including decreased synaptic connections (p<0.05), in 3rd instar larvae which were developed in space. Furthermore, space-grown microgravity adults show a decrease in neuronal (p<0.05) and dendritic field (p<0.01) in adult brains coupled with an increased number of apoptotic cells (p<0.001) compared to in-flight 1g controls, suggesting increased neuronal loss under spaceflight conditions. In summary, we observe that altered gravity leads to gross neurological deficits. To better understand the long-term effects of spaceflight on the nervous system, longitudinal and multigenerational changes were also identified. This study will help elucidate the different approaches to prevent nervous system dysfunction in astronauts during spaceflight, while also contributing to a better understanding of the pathways that are related to some CNS disorders on Earth.

Iyer, Janani↗
NASA NTRS1990

Influence of single hindlimb support during simulated weightlessness in the rat

A study was carried out to develop and evaluate a hindlimb suspension model, making it possible to differentiate the effects of non-weight bearing by hindlimbs per se from the systemic influence of simulated weightlessness. A support platform was designed which allowed the animal to maintain one hindlimb in a posture similar to the hindlimbs of the control animals at rest and to maintain one hindlimb in a posture similar to the hindlimbs of the control animals, providing a support for the animal to contract or stretch hindlimb muscles against at any time during suspension. The results of this study indicated that hindlimb support during head-down suspension will maintain muscle-mass/body-mass ratios, glycogen concentration, and blood flow. However, it will not prevent the loss in citrate synthase activity associated with conditions of simulated weightlessness.

Stump, Craig S.↗
NASA NTRS2003

Macromolecular Expression and Function: A New Paradigm for NASA Risk Assessment

Predicting risks in humans of either acute effects such as bone loss or muscle wasting, or late effects such as cancer, is challenging. To an approximation, this is because uncertainties of exposure to stress factors or toxic agents and the uniformity of processing subsequent damage at the cellular level within a complex set of biological variables degrade the confidence of predicting pathologic outcome. A cellular biodosimeter that simultaneously reports 1) the type of damage due to that exposure, 2) the quantity of damage incurred by that exposure, and 3) the dataset used to assess risk of developing pathologic outcome caused by that exposure would therefore be useful for predicting ultimate risks faced by an individual, such as an astronaut. It is suggested that such a biodosimeter can be based upon analyses of gene-expression and protein expression whereby large datasets of cellular response to damage are obtained and analyzed for expression-profiles correlated with established end points and molecular markers predictive for risks being assessed. The usefulness of multiparametric cellular biodosimeters could be realized by quantitatively profiling these datasets using techniques of bioinformatics. Such an approach contributes to the foundation of molecular epidemiology as a new scientific discipline, and represents a new paradigm of risk assessment.

Richmond, Robert↗
NASA NTRS1998

Evolution of the vestibulo-ocular system

The evolutionary and developmental changes in the eye muscle innervation, the inner ear, and the vestibulo-ocular reflex are examined. Three eye muscle patterns, based on the innervation by distinct ocular motoneurons populations, can be identified: a lamprey, an elasmobranch, and a bony fish/tetrapod pattern. Four distinct patterns of variation in the vestibular system are described: a hagfish pattern, a lamprey pattern, an elasmobranch pattern, and a bony fish/tetrapod pattern. Developmental data suggest an influence of the hindbrain on ear pattern formation, thus potentially allowing a concomitant change of eye muscle innervation and ear variation. The connections between the ear and the vestibular nuclei and between the vestibular nuclei and ocular motoneurons are reviewed, and the role of neurotrophins for pattern specification is discussed. Three patterns are recognized in central projections: a hagfish pattern, a lamprey pattern, and a pattern for jawed vertebrates. Second-order connections show both similarities and differences between distantly related species such as lampreys and mammals. For example, elasmobranchs lack an internuclear system, which is at best poorly developed in lampreys. It is suggested that the vestibulo-ocular system shows only a limited degree of variation because of the pronounced functional constraints imposed on it.

Non-NASA Center↗
NASA NTRS2000

Electroactive Polymers as Artificial Muscles: Capabilities, Potentials and Challenges

The low density and the relative ease of shaping made polymers highly attractive materials and they are increasingly being chosen for aerospace applications. Polymer matrix composite materials significantly impacted the construction of high performance aircraft components and structures. In recent years, the resilience characteristics of polymers made them attractive to the emerging field of inflatable structures. Balloons were used to cushion the deployment of the Mars Pathfinder lander on July 4, 1997, paving the way for the recent large number of related initiatives. Inflatable structures are now being used to construct a rover, aerial vehicles, telescopes, radar antennas, and others. Some of these applications have reached space flight experiments, whereas others are now at advanced stages of development.

Bar-Cohen, Yoseph↗
NASA NTRS2003

Mechanical injury and repair of cells

OBJECTIVE: To concisely review the field of cell plasma membrane disruption (torn cell surface) and repair. MAIN POINTS: Plasma membrane disruption is a common form of cell injury under physiologic conditions, after trauma, in certain muscular dystrophies, and during certain forms of clinical intervention. Rapid repair of a disruption is essential to cell survival and involves a complex and active cell response that includes membrane fusion and cytoskeletal activation. Tissues, such as cardiac and skeletal muscle, adapt to a disruption injury by hypertrophying. Cells adapt by increasing the efficiency of their resealing response. CONCLUSION: Plasma membrane disruption is an important cellular event in both health and disease. The disruption repair mechanism is now well understood at the cellular level, but much remains to be learned at the molecular level. Cell and tissue level adaptational responses to the disruption either prevent its further occurrence or facilitate future repairs. Therapeutically useful drugs might result if, using this accumulating knowledge, chemical agents can be developed that can enhance repair or adaptive responses.

Review, Tutorial↗
NASA NTRS1994

Eccentric exercise testing and training

Some researchers and practitioners have touted the benefits of including eccentric exercise in strength training programs. However, others have challenged its use because they believe that eccentric actions are dangerous and lead to injuries. Much of the controversy may be based on a lack of understanding of the physiology of eccentric actions. This review will present data concerning eccentric exercise in strength training, the physiological characteristics of eccentric exercise, and the possible stimulus for strength development. Also a discussion of strength needs for extended exposure to microgravity will be presented. Not only is the use of eccentric exercise controversial, but the name itself is fraught with problems. The correct pronunciation is with a hard 'c' so that the word sounds like ekscentric. The confusion in pronunciation may have been prevented if the spelling that Asmussen used in 1953, excentric, had been adopted. Another problem concerns the expressions used to describe eccentric exercise. Commonly used expressions are negatives, eccentric contractions, lengthening contractions, resisted muscle lengthenings, muscle lengthening actions, and eccentric actions. Some of these terms are cumbersome (i.e., resisted muscle lengthenings), one is slang (negatives), and another is an oxymoron (lengthening contractions). Only eccentric action is appropriate and adoption of this term has been recommended by Cavanagh. Despite the controversy that surrounds eccentric exercise, it is important to note that these types of actions play an integral role in normal daily activities. Eccentric actions are used during most forms of movement, for example, in walking when the foot touches the ground and the center of mass is decelerated and in lowering objects, such as placing a bag of groceries in the car.

Clarkson, Priscilla M.↗
NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗