Tau approximation techniques for identification of coefficients in parabolic PDE
A variant of the Tau method, called the weak Tau method, is developed on the basis of the weak form of the PDE for use in least-squares parameter estimation; also presented is a suitable abstract convergence framework. The emphasis is on the theoretical framework that allows treatment of the weak Tau method when it is applied to a wide class of inverse problems, including those for diffusion-advection equations, the Fokker-Planck model for population dynamics, and damped beam equations. Extensive numerical testing of the weak Tau method has demonstrated that it compares quite favorably with existing methods.
Banks, H. T.↗