AN EFFICIENT SPACE-TIME ADAPTIVE WAVELET GALERKIN METHOD FOR TIME-PERIODIC PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

摘要

We introduce a multitree-based adaptive wavelet Galerkin algorithm for space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin nature of the variational formulation and present numerical results for the heat and a convection-diffusion-reaction equation.