Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
For researchers in numerical analysis and computational PDEs, this work offers rigorous theoretical guarantees for a diffuse interface method on moving surfaces.
The paper provides stability and error analysis for a fully discrete numerical scheme solving a parabolic PDE on a moving surface using a diffuse interface approach, with error bounds confirmed by test calculations.
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis.