JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Analysis of a Non-standard Finite Element Method Based on Boundary Integral Operators
نویسندگان
چکیده
We present and analyze a non-standard finite element method based on elementlocal boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit knowledge of the fundamental solution of the partial differential operator, but only locally, i.e. in every polyhedral element. This allows us to solve PDEs with elementwise constant coefficients. In this paper we consider the diffusion equation as a model problem, but the method can be generalized to convection-diffusion-reaction problems and to systems of PDEs like the linear elasticity system with elementwise constant coefficients. We provide a rigorous error analysis of the method under quite general assumptions on the geometric properties of the elements. Numerical results confirm our theoretical estimates.
منابع مشابه
JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics FETI Solvers for Non-Standard Finite Element Equations Based on Boundary Integral Operators
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