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Local flux mimetic finite difference methods. (English) Zbl 1165.65063

The authors use a MFPA-type construction to develop new cell-centered discretization methods on polyhedral meshes for diffusion problems with full tensor coefficients. Under a few constructive assumptions they prove first-order convergence for both the velocity and the pressure variables, as well as second-order superconvergence for the pressure variable in discrete \(L^2\) norms.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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