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The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes. (English) Zbl 1120.65332
Summary: We study the mimetic finite difference discretization of diffusion-type problems on unstructured polyhedral meshes. We demonstrate high accuracy of the approximate solutions for general diffusion tensors, the second-order convergence rate for the scalar unknown and the first order convergence rate for the vector unknown on smooth or slightly distorted meshes, on non-matching meshes, and even on meshes with irregular-shaped polyhedra with flat faces. We show that in general the meshes with non-flat faces require more than one flux unknown per mesh face to get optimal convergence rates.
65N06Finite difference methods (BVP of PDE)
76M20Finite difference methods (fluid mechanics)
65N12Stability and convergence of numerical methods (BVP of PDE)