The curved mimetic finite difference method: Allowing grids with curved faces
Journal of Computational Physics, 2023 We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of ...
Pitassi S. +4 more
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A Higher-Order Formulation of the Mimetic Finite Difference Method
SIAM Journal on Scientific Computing, 2008 A new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes. This approach provides a higher-order accurate approximation to the flux of the exact solution. In analogy with the original formulation, a family of local scalar products is constructed to satisfy the fundamental ...
L. Beirao da Veiga, G. Manzini
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Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes [PDF]
SIAM Journal on Numerical Analysis, 2005 The stability and convergence properties of the mimetic finite difference method for diffusion-type 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.
Brezzi F, Lipnikov K, Shashkov M
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Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals [PDF]
SIAM Journal on Numerical Analysis, 2005 Summary: Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over \(h^2\)-uniform quadrilateral meshes. The superconvergence holds for a full tensor coefficient. The analysis exploits a relation between mimetic finite differences and mixed finite element methods via a special ...
Berndt, M. +4 more
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Mimetic finite difference method for the Stokes problem on polygonal meshes [PDF]
Journal of Computational Physics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L. Beirao da Veiga +3 more
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Numerical results for mimetic discretization of Reissner-Mindlin plate problems [PDF]
, 2012 A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated.
da Veiga, Lourenco Beirao +2 more
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A mortar mimetic finite difference method on non-matching grids [PDF]
Numerische Mathematik, 2005 This paper deals with the mimetic finite difference (MFD) method on nonmatching multiblock grids for second-order linear elliptic equation with Dirichlet boundary conditions. The authors establish a relation between the mortar MFD method and mortar mixed finite element methods.
Berndt, Markus +4 more
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An Efficient Hybrid Model for Nonlinear Two-Phase Flow in Fractured Low-Permeability Reservoir
Energies, 2019 The staged fracturing horizontal well has proven to be an attractive alternative for improving the development effect of a low permeability waterflood reservoir.
Daigang Wang +3 more
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Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes [PDF]
, 2014 Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive
Bonelle, Jerome, Ern, Alexandre
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Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection [PDF]
, 2013 Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead to a ...
Paulino, Glaucio H., Talischi, Cameron
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