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Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes. (English) Zbl 1057.65071

Summary: Mimetic discretizations based on the support-operators methodology are derived for non-orthogonal locally refined quadrilateral meshes. The second-order convergence rate on non-smooth meshes is verified with numerical examples.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
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References:

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