Arbitrary order BEM-based Finite Element Method on polygonal meshes
نویسنده
چکیده
Polygonal meshes show up in more and more applications and the BEMbased Finite Element Method turned out to be a forward-looking approach. The method uses implicitly defined trial functions, which are treated locally by means of Boundary Element Methods (BEM). Due to this choice the BEM-based FEM is applicable on a variety of meshes including hanging nodes. The aim of this presentation is to give a rigorous construction of H1-conforming trial functions yielding arbitrary order of convergence in a Finite Element Method for elliptic equations. With the help of an interpolation operator, approximation properties are proven which guaranty optimal rates of convergence in the H1as well as in the L2-norm for FEM simulations. These theoretical results are illustrated and verified by several numerical examples on polygonal meshes.
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