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) |
Keywords:
mimetic finite differences;quadrilateral meshes;diffusion equation;mesh refinement;convergence;numerical examplesSoftware:
AMG1R5Cite
Full Text:DOI
References:
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