An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations

TL;DR

This paper presents a space-time adaptive wavelet Galerkin method for efficiently solving time-periodic parabolic PDEs, achieving optimal convergence rates with linear complexity and demonstrating broad applicability through numerical experiments.

Contribution

It introduces a multitree-based adaptive wavelet Galerkin algorithm tailored for space-time discretization of time-periodic parabolic PDEs, addressing implementation challenges and proving optimal convergence.

Findings

Method converges with the best possible rate

Achieves linear computational complexity

Successfully applied to heat and convection-diffusion-reaction equations

Abstract

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.