Finite Element Analysis for bulk–surface Partial Differential Equations in evolving Domains

Abstract

This dissertation studies the numerical approximation of various partial bulk–surface differential equations in time-dependent domains. The main interest is an application to a model of tissue growth which is a slight modification of a model presented by Eyles, King & Styles [2019]. The model couples a Poisson equation in the time-dependent domain with a forced mean curvature flow of the free boundary surface, with nontrivial bulk–surface coupling in both the velocity law of the evolving boundary surface and the boundary condition of the Poisson equation.