A quasi-optimal space-time FEM with local mesh refinements for parabolic problems

TL;DR

This paper introduces a space-time finite element method for the heat equation that achieves near-optimal accuracy and efficiently handles local mesh refinements using advanced iterative solvers.

Contribution

It presents a novel quasi-optimal space-time FEM with local mesh refinement capabilities and an efficient conjugate gradient solver with an optimal preconditioner.

Findings

Achieves quasi-optimal approximation in natural norms.

Effectively incorporates local mesh refinements.

Uses a conjugate gradient method with an (almost) optimal preconditioner.

Abstract

We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a conjugate gradient method with a (nearly) optimal preconditioner.