Mimetic finite difference methods for Hamiltonian wave equations in 2D
Computers & Mathematics with Applications, 2017 In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in time to integrate the semi-discrete Hamiltonian system.
Beirao da Veiga, L. +2 more
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A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS [PDF]
Mathematical Models and Methods in Applied Sciences, 2010 We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of
Droniou, Jerome +3 more
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A finite element framework for some mimetic finite difference discretizations
Computers & Mathematics with Applications, 2015 submitted
Rodrigo, Carmen +3 more
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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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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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A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems [PDF]
, 2014 We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve ...
Antonietti, Paola F. +2 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
core +1 more source
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
openaire +2 more sources
Destruction of the family of steady states in the planar problem of Darcy convection [PDF]
, 2008 The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states.
Arakawa +17 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
doaj +1 more source