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Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems
SIAM Journal on Numerical Analysis, 2009We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes.
Cangiani A, Manzini G, Russo A
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Convergence analysis of the high-order mimetic finite difference method
Numerische Mathematik, 2009The paper deals with the numerical solution of a second order elliptic problem with the aid of the mimetic finite difference (MFD) method. The elliptic operator has to be strongly elliptic. The author proves a priori error estimates, namely the second order of convergence of the conservative variable and its flux.
Beirao da Veiga +3 more
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A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
Mathematical Models and Methods in Applied Sciences, 2005A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoretical results are confirmed with numerical experiments.
F. Brezzi +2 more
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A residual based error estimator for the Mimetic Finite Difference method
Numerische Mathematik, 2007The author presents a local error indicator for the mimetic finite difference method for diffusion problems on general polyhedral meshes. The diffusion problem is expressed as a system of a vector and a scalar field. The error indicator is defined elementwise from the local residual and the error due to the discretization of the right hand side of the ...
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Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem
Lobachevskii Journal of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abushaikha, A., Terekhov, K
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Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics
Computer Methods in Applied Mechanics and Engineering, 2021Andrea Borio +2 more
exaly
Mimetic Finite Difference Methods for Convection-Dominated Problems
Communications to SIMAI Congress, 2006Andrea Cangiani +2 more
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