Comparison of Two Couplings of the Finite Volume Method and the Boundary Element Method

Erath, Christoph

doi:10.1007/978-3-319-05684-5_24

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“…This problem is the classical Laplace problem for the interior and exterior domain and one can see this as a benchmark problem to test new discrete systems, especially with adaptive mesh refinement techniques. In [17] the reader can find a comparison between the adaptive FVM-BEM approach of [16] and the adaptive cell-centered FVM-BEM with a conforming Morley interpolant in [15]. Therefore we compare the results of the coupling in this work, where we use the nonconforming Morley interpolant (noco) for the post processed finite volume solution, against the adaptive coupling given in [15], where we used a conforming Morley interpolant (co); i.e., a Morley element for diffusion problems.…”

Section: Mexican Hat Problemmentioning

confidence: 99%

A nonconforming a posteriori estimator for the coupling of cell-centered finite volume and boundary element methods

Erath

2014

Numer. Math.

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The coupling of the cell-centered finite volume method and the boundary element method is an interesting approach to solve elliptic problems on an unbounded domain, where local flux conservation is important. Based on the piecewise constant interior finite volume solution we define a Morley-type interpolant built on a nonconforming finite element. Together with the Cauchy data of the exterior boundary element solution this allows us to define a residual-based a posteriori error estimator. With respect to an energy norm we prove reliability and efficiency of this estimator and use its local contributions to steer an adaptive mesh-refining algorithm. In two examples we illustrate the effectiveness of the new adaptive coupling method and compare it with the coupling approach with a conforming Morley interpolant.Mathematics Subject Classification 65N08 · 65N38 · 65N15 · 65N50 · 76M12 · 76M15

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