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The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
SIAM Journal on Numerical Analysis, 1999Summary: Accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations.
Hyman, James M., Shashkov, Mikhail
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Flux reconstruction and solution post-processing in mimetic finite difference methods
Computer Methods in Applied Mechanics and Engineering, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cangiani, A., Manzini, G. M.
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M-Adaptation in the mimetic finite difference method [PDF]
Mathematical Models and Methods in Applied Sciences, 2014 The mimetic finite difference method produces a family of schemes with equivalent properties such as the stencil size, stability region, and convergence order. Each member of this family is defined by a set of parameters which can be chosen locally for every mesh element. The number of parameters depends on the geometry of a particular mesh element. M-
V. Gyrya +3 more
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Mimetic Finite Difference Methods for Diffusion Equations
Computational Geosciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hyman, J. +3 more
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Geoelectric data modeling using Mimetic Finite Difference Method
2022<p><span>Nondestructive imaging and monitoring of the earth's subsurface using the geoelectric method require reliable and versatile numerical techniques for solving differential equation that govern the method's physic.
Deepak Suryavanshi, Rahul Dehiya
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Nodal Mimetic Finite Difference Methods
2018GDMs are obtained from the nodal mimetic finite differences methods, and also cover some DDFV schemes.
Jérôme Droniou +4 more
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Foundations of mimetic finite difference method
2014The mimetic discretization technology relies on a discrete vector and tensor calculus (DVTC) that deals with discrete fields and discrete operators. The DVTC makes it possible to reproduce (or mimic) fundamental identities of continuum calculus, such as kernels of operators (see Sect. 2.6) and the Helmholtz decomposition theorems (see Sect.
Lourenço Beirão da Veiga +2 more
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The Mimetic Finite Difference Method for Elliptic Problems
2014This book offers a systematic and thorough examination of theoretical and computational aspects of the modem mimetic finite difference (MFD) method. The MFD method preserves or mimics underlying properties of physical and mathematical models, thereby improving the fidelity and predictive capability of computer simulations.
L. Beirao da Veiga +2 more
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Benchmark 3D: A Mimetic Finite Difference Method
2011In the two-dimensional discretisation benchmark session at the FVCA5 conference, we participated with a Mimetic Finite Difference (MFD) method [7]. In this paper, we present results for the three-dimensional case using the same method. Since the previous conference, the equivalence of MFD, Hybrid Finite Volume and Mixed Finite Volume methods has been ...
Peter Bastian +2 more
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Benchmark 3D: Mimetic Finite Difference Method for Generalized Polyhedral Meshes
2011Let ? be a subset of R3 with a Lipschitz continuous boundary. We consider the mixed (velocity-pressure) formulation of the diffusion problem.
K Lipnikov, G Manzini
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