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Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems. (English) Zbl 1015.65068

A mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order partial differential equations in the state variable and its flux is constructed and analyzed. An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated-Q1 nonconforming space. Furthermore, it is demonstrated that the present finite volume method can be interpreted as a rotated-Q1 nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage

Software:

TOUGH
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