×

Convergence analysis on quadrilateral grids of a DDFV method for subsurface flow problems in anisotropic heterogeneous porous media with full Neumann boundary conditions. (English) Zbl 1488.35206

Summary: Our purpose in this paper is to present a theoretical analysis of the Discrete Duality Finite Volume method (DDFV method) for 2D-flow problems in anisotropic heterogeneous porous media with full Neumann boundary conditions. We start with the derivation of the discrete problem, and then we give a result of existence and uniqueness of a solution for that problem. Their theoretical properties, namely stability and error estimates in discrete energy norms and \(L^2\)-norm are investigated. Numerical tests are provided.

MSC:

35J25 Boundary value problems for second-order elliptic equations
65N08 Finite volume methods for boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
PDFBibTeX XMLCite
Full Text: Euclid