2022/01/01 by Charles M. Elliott, Harald Garcke, Elliott, Charles M. +3 · 2 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2202.03302
openalex publication_date 2022/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the H1 norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.