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arXiv · 1502.05954

Convection-adapted BEM-based FEM

Clemens Hofreither·Ulrich Langer·Steffen Weißer
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Abstract

We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness matrices are constructed by means of local boundary element techniques. Our method, which we refer to as a BEM-based FEM, can therefore be considered a local Trefftz method with element-wise (locally) PDE-harmonic shape functions. The Dirichlet boundary data for these shape functions is chosen according to a convection-adapted procedure which solves projections of the PDE onto the edges and faces of the elements. This improves the stability of the discretization method for convection-dominated problems both when compared to a standard FEM and to previous BEM-based FEM approaches, as we demonstrate in several numerical experiments.

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Clemens Hofreither, Ulrich Langer, Steffen Weißer. 2015-02-20. Convection-adapted BEM-based FEM. https://doi.org/10.1002/zamm.201500042

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