Immersed interface method for a level set formulation of problems with moving boundaries

Abstract

The motivation of this study is a numerical solution of Laplace equation on a time dependent domain that contains a moving boundary evolving with a speed depending on the gradient rp. We use a level set formulation of this problem and propose an immersed interface method for the numerical solution of some partial dierential equations solve in the level set formulation. This paper can be seen as an accompanying publication to [4] where an application to groundwater  ow with dynamic water table is studied. Additionally to [4], technical details of the level set and immersed interface method are given and a new numerical experiment is provided.