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Preprint-No.: <   342   >   Published in: June 2012   PDF-File: IGPM342_k.pdf
Title:A Volume Mesh Finite Element Method for PDEs on Surfaces
Authors:Maxim A. Olshanskii, Arnold Reusken , and 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
(2012)