Accessible Requires Authentication Published by De Gruyter January 1, 2012

A Note on the Convergence Analysis of a Diffuse-domain Approach

Sebastian Franz, Hans-Görg Roos, Roland Gärtner and Axel Voigt

Abstract

We analyse the error behaviour of a diffuse-domain approximation of an elliptic differential equation. In one dimension and for a half-plane problem in two dimensions an approximation quality of order one in the interface parameter is shown. Some supporting numerical experiments are also presented.

Received: 2011-12-15
Revised: 2012-03-23
Accepted: 2012-03-27
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus