Cut Finite Element Methods for Coupled Bulk-Surface Problems

Abstract

We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic system of equations has a similar condition number as a standard fitted finite element method. Finally, we present a numerical example illustrating the accuracy and the robustness of our approach.

References in corpus (3)

• A stabilized cut finite element method for partial differential equations on surfaces: The Laplace-Beltrami operator
• A stabilized Nitsche fictitious domain method for the Stokes problem
• A cut finite element method for a Stokes interface problem

Cited by in corpus (1)

• A trace finite element method for a class of coupled bulk-interface transport problems