A diffuse interface box method for elliptic problems

G. Negrini; N. Parolini; M. Verani

doi:10.1016/j.aml.2021.107314

paper

A diffuse interface box method for elliptic problems

arXiv:2101.11339 · doi:10.1016/j.aml.2021.107314

Abstract

We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori $H^{1}$ and $L^{2}$ error estimates highlighting the rôle of the mesh discretization parameter and of the diffuse interface width. Finally, we present a numerical result assessing the theoretical findings.

10 pages, 5 figures, submitted on Applied Mathematics Letters