I will be giving a talk at the Free Boundary Problems 2021 meeting as part of the Coupled Surface-Bulk problem mini-symposium.

Numerical analysis of a coupled bulk-surface problem in an evolving domain

Abstract

Based on an abstract theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains, I will present numerical analysis of a simple coupled bulk-surface problem. The problem couples a linear parabolic equation in the evolving bulk domain to a linear parabolic equation posed on the boundary surface of the domain. Evolving bulk and surface isoparametric finite element spaces defined on evolving triangulations will be developed.Optimal a priori bounds are shown under usual assumptions on the geometry and solution of the partial differential equation.We conclude with a numerical example.

Slides

Funding

This work was supported by a Leverhulme Trust early career fellowship.