Mimetic finite difference method

By Konstantin Lipnikov, Gianmarco Manzini, Mikhail Yu. Shashkov. Journal of Computational Physics, 2014

471 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4ef21f3b830db7307cd754b39589211adf7e4135

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In Computational Mechanics

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Citations in the corpus

Hourglass stabilization and the virtual element method (2015, background): “The connection with mimetic discretizations [21] is discussed in Reference [22].”
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.”
On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2013, background): “satisfaction of a discrete maximum principle or improvement of performance of algebraic solvers) as illustrated in [36,37].”
Conforming and nonconforming virtual element methods for elliptic problems (2015, unknown): “The VEM approach can also be viewed as a variational analogue of the mimetic finite difference (MFD) method; see [10] and the recent review paper [30].”
SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations (2018, methodology): “A survey on the MFD method can be found in the review paper [6] and the research book [7].”
The nonconforming virtual element method (2014, methodology): “Among them the mimetic finite difference (MFD) method that has been successfully applied to a wide range of scientific and engineering applications (see, for instance, [17, 28, 33, 29] and the references therein).”
A virtual element method with arbitrary regularity (2014, methodology): “…and nodal MFD methods allow us to extend mimetic technology (see, for example, Brezzi et al., 2005a,b, 2009; Beirão da Veiga, 2008, 2010; Beirão da Veiga & Manzini, 2008; Cangiani & Manzini, 2008; Beirão da Veiga et al., 2009a,b, 2011b; Cangiani et al., 2009; Lipnikov et al., 2011) to the VEM.”
A multigrid algorithm for the $p$-version of the Virtual Element Method (2017, methodology): “Examples of methods that have been proposed so far include mimetic finite differences [20, 35, 51, 52], polygonal finite element methods [58, 59], discontinuous-Galerkin finite element methods [4, 5, 9, 16, 37, 38, 40] hybridizable and hybrid high hrder methods [42, 43, 45], BEM-based FEM [56] and g”
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.”
A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method (2016, methodology): “112 Borrowing ideas from the Mimetic Finite Difference method [30, 31], the 113 VEM can be regarded as a generalization of regular finite elements to meshes 114 made up by polygonal elements of any number of edges.”
MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA (2016, methodology): “We refer to [14] and [45] for a comprehensive review on MFD schemes.”