Titlebook: BEM-based Finite Element Approaches on Polytopal Meshes; Steffen Wei?er Book 2019 Springer Nature Switzerland AG 2019 BEM-based FEM.Trefft

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Finite Element Method on Polytopal Meshes,nd engineering. The approach relies on the decomposition of the underlying domain into elements and the construction of a discrete approximation space over the given discretization. The BEM-based finite element method can be seen as a generalization in order to handle more general elements in the me

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Boundary Integral Equations and Their Approximations,a short introduction into this topic with a special emphasis on its application in the BEM-based FEM. Therefore, the boundary integral operators for the Laplace problem are reviewed in two- and three-dimensions and corresponding boundary integral equations are derived. Their discretization is realiz

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Book 2019 meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and

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Introduction,locally refined meshes with naturally included hanging nodes, and to convection-diffusion-reaction problems, showing stabilizing effects while incorporating the differential equation into the approximation space. All theoretical considerations are substantiated with several numerical tests and examples.

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Michael A. Tallon,Xuejun (Jay) Liuver these general meshes. The formulation of the BEM-based FEM is obtained by means of a Galerkin formulation and its convergence and approximation properties are analysed with the help of introduced interpolation operators. Numerical experiments confirm the theoretical findings.