Tau approximation techniques for identification of coefficients in parabolic PDE

The authors introduce a variant of the Tau method, called the weak Tau method, which is based on the weak form of the partial differential equation (PDE), for use in least-squares parameter estimation, and they present 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. The authors have carried out extensive numerical testing of the weak Tau method and found that it compares quite favorably with existing methods