Mimetic finite differences for elliptic problems

By Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov. 2009

204 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/181d28d53f075ae40eeafed29e9eb8f7b51feb76

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In Computational Mechanics

In Mechanics of Materials

In Numerical Analysis

Citations in the corpus

Orthogonal polynomials in badly shaped polygonal elements for the Virtual Element Method (2017, unknown): “The Virtual Element Method was recently developed as a generalization of Mimetic Finite Differences,[29, 30], and has been applied to a wide number of problems, such as plate bending problems [31], elasticity problems [32, 33], Stokes problems [34] and the Steklov eigenvalue problem [35].”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “We refer to the recent papers and monographs [19, 8, 17, 9, 13, 15, 28, 30, 31, 33, 35, 34, 36, 39, 40, 24, 32, 21] as a brief representative sample of the increasing list of technologies that make use of polygonal/polyhedral meshes.”
Mimetic finite difference method (2014, background): “The presentation is based on [26] [29] [52].”
A virtual element method with arbitrary regularity (2014, methodology): “These goals may be achieved while still keeping the property of mesh generality of mimetic finite difference (MFD) methods; see, for example, the mixed and primal formulations given in Brezzi et al. (2005a, 2009) and Beirão da Veiga et al. (2011b).”
Virtual Elements for Linear Elasticity Problems (2013, background): “As for the traditional mimetic finite difference approach the decomposition of the computational domain Ω can be done in a very general way as, for instance, in [11].”
The Hitchhiker's Guide to the Virtual Element Method (2014, background): “On the other hand, many of its aspects are closely connected with Finite Volume Methods (see for instance [19,20,28,32]) and in particular with Mimetic Finite Differences (MFD) [2–4, 7, 10, 12, 14–16, 18, 22, 23, 25–27].”
The nonconforming virtual element method (2014, methodology): “The VEM allows one to recast the MFD schemes [14, 7] as Galerkin formulations.”
Small-stencil 3D schemes for diffusive flows in porous media (2012, methodology): “Note that the same type of idea was also used in [10].”
New perspectives on polygonal and polyhedral finite element methods (2014, background): “A representative list of problems treated using MFD includes electromagnetism [104, 105, 106, 107, 108], continuum mechanics [109], gas dynamics [110, 111], linear diffusion in primal form [112, 113], convectiondiffusion [114, 115], Stokes flow [116, 117, 118, 119], elasticity [120], Reissner-Mindli”
MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA (2016, methodology): “Thanks to their great flexibility and their capability of preserving the fundamental properties of the underlying physical and mathematical models, the use of MFD methods has remarkably increased in the last years, with application to diffusion-type problems [23, 26, 24, 25, 21, 14, 7], electromagne”
Residual a posteriori error estimation for the Virtual Element Method for elliptic problems (2015, methodology): “The Virtual Element Method has also a relation with the Mimetic Finite Difference (MFD) schemes, for a very short list see for instance [6, 18, 20, 23, 26, 28] and the book [13] with the references therein.”