Adaptive finite elements for semilinear reaction-diffusion systems on growing domains

TL;DR

This paper introduces an adaptive finite element method for solving reaction-diffusion systems on evolving domains, with a focus on error estimation and validation through benchmarks.

Contribution

It develops a new error estimator for adaptive finite element methods applied to reaction-diffusion systems on moving domains.

Findings

Error estimator effectively bounds the approximation error.

Method accurately captures solutions on time-dependent domains.

Benchmark results confirm theoretical predictions.

Abstract

We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimator that provides an upper bound for the error in the semidiscrete (space) scheme. We reconcile our theoretical results with benchmark computations.