Optimal space-time adaptive wavelet methods for degenerate parabolic PDEs (Q431301)

The purpose of this work is to analyze certain types of degenerate linear parabolic differential equations (PDEs) and to propose an algorithm for their numerical treatment. A weak space-time formulation for the problem with singular or degenerate time-dependent coefficients is considered and the existence of a unique weak solution is proved. Then, the discretization of the degenerate parabolic PDE is presented using space-time wavelets. An optimality result for the iterative solution of the arising systems is obtained.