342 RWTH Publication No: 47266        2012        IGPM342.pdf
TITLE A Volume Mesh Finite Element Method for PDEs on Surfaces
AUTHORS Maxim A. Olshanskii, Arnold Reusken , Xianmin Xu
ABSTRACT We treat a surface finite element method that is based on the trace of a standard finite element space on a tetrahedral triangulation of an outer domain that contains a stationary 2D surface. This surface FEM is used to discretize partial differential equation on the surface. We demonstrate the performance of this method for stationary and time-dependent diffusion equations. For the stationary case, results of an adaptive method based on a surface residual-type error indicator are presented. Furthermore, for the advection-dominated case a SUPG stabilization is introduced. The topic of finite element stabilization for advection-dominated surface transport equations has not been addressed in the literature so far.
KEYWORDS surface finite element, surface SUPG stabilization, residual-type surface finite element error indicator
PUBLICATION ECCOMAS 2012 : September 10 - 14, 2012,
Vienna, Austria ;
proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering / organized by Vienna University of Technology