An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Elliott, Charles M., Sales, Thomas
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866915487850430464
author Elliott, Charles M.
Sales, Thomas
author_facet Elliott, Charles M.
Sales, Thomas
contents In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time discretisation. Our analysis relies on a specific geometric assumption on the evolution of the surface. Our main results are $L^2_{H^1}$ error bounds for both the semi-discrete and fully discrete schemes, and we provide some numerical results.
format Preprint
id arxiv_https___arxiv_org_abs_2411_05650
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential
Elliott, Charles M.
Sales, Thomas
Numerical Analysis
65M60 (Primary) 65M16, 35K67 (Secondary)
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward Euler time discretisation. Our analysis relies on a specific geometric assumption on the evolution of the surface. Our main results are $L^2_{H^1}$ error bounds for both the semi-discrete and fully discrete schemes, and we provide some numerical results.
title An evolving surface finite element method for the Cahn-Hilliard equation with a logarithmic potential
topic Numerical Analysis
65M60 (Primary) 65M16, 35K67 (Secondary)
url https://arxiv.org/abs/2411.05650