# A Stable Space-Time Finite Element Method for Parabolic Evolution Problems

## TL;DR

This paper introduces a new stable space-time finite element method for solving parabolic evolution problems in moving domains, providing theoretical error estimates and confirming them through numerical experiments.

## Contribution

The paper develops a novel stable space-time FEM approach for parabolic problems in moving domains, with rigorous error analysis and validation.

## Key findings

- The method is stable and elliptic in the discrete energy norm.
- Error estimates are derived and validated.
- Numerical experiments confirm theoretical predictions.

## Abstract

This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yields an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains to confirm the theory presented.