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Convergence of multipoint flux approximations on quadrilateral grids. (English) Zbl 1106.76043

Summary: This article presents a convergence analysis of the multipoint flux approximation control volume method, MPFA, in two space dimensions. The MPFA version discussed here is the so-called \(O\)-method on general quadrilateral grids. The discretization is based on local mappings onto a reference square. The key ingredient in the analysis is an equivalence between the MPFA method and a mixed finite element method, using a specific numerical quadrature, such that the analysis of the MPFA method can be done in a finite element setting.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

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