Error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface

30 November 2017
Dr Vanessa Styles

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. Test calculations are presented that confirm our analysis.

  • Computational Mathematics and Applications Seminar