A Note on the Convergence Analysis of a Diffuse-domain Approach
Sebastian Franz, Hans‐Görg Roos, Roland Gärtner, Axel Voigt · Computational Methods in Applied Mathematics · 2012
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.