A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations

Abstract

In this work, an $r$-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-in-time and (locally refined) finite element spaces-in-space. Numerical results illustrate our theoretical findings.

References in corpus (6)

• Further results on a space-time FOSLS formulation of parabolic PDEs
• On the Sobolev and $L^p$-Stability of the $L^2$-projection
• Accuracy controlled data assimilation for parabolic problems
• A parallel algorithm for solving linear parabolic evolution equations
• Near-best adaptive approximation on conforming meshes
• Massively parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations

Cited by in corpus (5)

• Improved rates for a space-time FOSLS of parabolic PDEs
• Interpolation Operator on negative Sobolev Spaces
• A well-posed First Order System Least Squares formulation of the instationary Stokes equations
• Accuracy controlled data assimilation for parabolic problems
• A parallel algorithm for solving linear parabolic evolution equations