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Mimetic Finite Difference Methods for Diffusion Equations
, 2001
"... This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous nonisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor ..."
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Cited by 61 (12 self)
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This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous nonisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor
Local flux mimetic finite difference methods
, 2005
"... We develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral grids. To approximate the flux (vector variable), the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per (ngon) el ..."
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Cited by 24 (7 self)
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We develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral grids. To approximate the flux (vector variable), the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per (n
Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes
 SIAM J. Numer. Anal
, 2007
"... The stability and convergence properties of the mimetic finite difference method for diffusiontype problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved. 1 ..."
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Cited by 95 (20 self)
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The stability and convergence properties of the mimetic finite difference method for diffusiontype problems on polyhedral meshes are analyzed. The optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved. 1
The Orthogonal Decomposition Theorems For Mimetic Finite Difference Methods
"... . 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. These methods mimic many fundamental properties o ..."
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Cited by 36 (10 self)
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. 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. These methods mimic many fundamental properties
Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals
 SIAM J. Numer. Anal
, 2004
"... Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of secondorder elliptic problems over h 2uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite d ..."
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Cited by 21 (14 self)
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Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of secondorder elliptic problems over h 2uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite
The Approximation of Boundary Conditions for Mimetic Finite Difference Methods
, 1997
"... We describe how to incorporate boundary conditions into finite difference methods so the resulting approximations mimic the identities between the differential operators of vector and tensor calculus. The approach is valid for wide class of partial differential equations of mathematical physics and ..."
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Cited by 21 (11 self)
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We describe how to incorporate boundary conditions into finite difference methods so the resulting approximations mimic the identities between the differential operators of vector and tensor calculus. The approach is valid for wide class of partial differential equations of mathematical physics
SUPERCONVERGENCE OF THE VELOCITY IN MIMETIC FINITE DIFFERENCE METHODS ON QUADRILATERALS
"... Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of secondorder elliptic problems over h2uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite ..."
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Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of secondorder elliptic problems over h2uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite
Mathematical Modeling and Analysis Convergence of Mimetic Finite Difference Method for Diffusion Problems on
"... In many applications meshes with general type elements are more preferable than standard tetrahedral or hexahedral meshes. Allowing arbitrary shape for a mesh element provides greater flexibility in the mesh generation process, especially in the regions where the geometry is extremely complex. For ..."
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cretization methods have been used. An example of such a method is the mimetic finite differ
Mathematical Modeling and Analysis Highorder Mimetic Finite Difference Methods on Arbitrary
"... The mimetic finite difference (MFD) methods mimic important properties of physical and mathematical models. As the result, conservation laws, solution symmetries, and the fundamental identities of the vector and tensor calculus are held for discrete models. The existing MFD methods for solving d ..."
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The mimetic finite difference (MFD) methods mimic important properties of physical and mathematical models. As the result, conservation laws, solution symmetries, and the fundamental identities of the vector and tensor calculus are held for discrete models. The existing MFD methods for solving
Results 1  10
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993,465