期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 50, 期 5, 页码 2357-2378出版社
SIAM PUBLICATIONS
DOI: 10.1137/110849481
关键词
BEM-based FEM; higher order scheme; polygonal mesh; generalized mesh; diffusion problem; Poisson equation
The BEM-based finite element method is reviewed and extended with higher order basis functions on general polygonal meshes. These functions are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients. They are treated by means of boundary integral formulations and are approximated using the boundary element method in the numerics. To obtain higher order convergence, a new approximation of the material coefficient is proposed since previous strategies are not sufficient. Following recent ideas, error estimates are proved which guarantee quadratic convergence in the H-1-norm and cubic convergence in the L-2-norm. The numerical realization is discussed and several experiments confirm the theoretical results.
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