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An adaptive nonsymmetric finite volume and boundary element coupling method for a fluid mechanics interface problem. (English) Zbl 1365.65237

Summary: We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the complement, an unbounded domain. Based on the nonsymmetric coupling of the finite volume method and boundary element method of C. Erath et al. [Numer. Math. 135, No. 3, 895–922 (2017; Zbl 1361.65083)] we introduce a semirobust residual error estimator. The upper bound of the error in an energy (semi)norm is robust against variation of the model data. The lower bound, however, additionally depends on the Péclet number and is therefore only semirobust. In several examples we use the local contributions of the a posteriori error estimator to steer an adaptive mesh-refining algorithm. The adaptive finite volume method-boundary element method coupling turns out to be an efficient method especially for solving problems from fluid mechanics, mainly because of the local flux conservation and the stable approximation of convection dominated problems.

MSC:

65N08 Finite volume methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76M15 Boundary element methods applied to problems in fluid mechanics

Citations:

Zbl 1361.65083

Software:

HILBERT
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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