A tensor artificial viscosity using a mimetic finite difference algorithm

By J. Campbell, Mikhail Yu. Shashkov. 2001

176 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/c3e8fb872ab9fa5e104480ec962363ba7b330bbf

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Mimetic finite differences for elliptic problems (2009, methodology): “In shock calculations, where the nodal discretization of an elliptic equation is used to add a numerical viscosity to the system [8], a non-symmetric breaking may quickly destroy solution symm etry.”
Equivalent projectors for virtual element methods (2013, background): “The origin of Virtual Elements, historically, is clearly from the classical Mimetic Finite Difference Method (see for instance [30, 26, 18, 27, 28]), and from their subsequent mathematical frameworks and settings [14, 16, 9, 15].”
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”
Virtual Elements for Linear Elasticity Problems (2013, background): “(For a partial list of citations we refer to [29, 25, 17, 24, 26, 13, 15, 8, 27, 1, 14, 6, 18, 21, 32, 11, 2, 10, 16].”
An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems (2008, methodology): “This kind of approximation methods have been successfully applied to a large range of different model problems: steady elliptic problems with anisotropic and rough diffusion tensors [1, 4] also using almost-arbitrary two-dimensional grids [5–8], electromagnetic problems [3, 9], flow simulations in p”
Basic principles of Virtual Element Methods (2013, background): “Since their very beginning, Mimetic Finite Differences (see for instance [28, 25, 17, 24, 26]), and in particular their mathematical frameworks and settings, have been evolving from the original Finite Difference/Finite Volumes point of view towards more Finite Element-like presentations and analyse”
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes (2005, methodology): “The MFD method has been successfully employed for solving pr oblems of continuum mechanics [18], electromagnetics [13], gas dynamics [7], and linear diffusion on simplicial and quadrilateral meshes in both the Cartesian and polar coordin ates [14, 12, 19, 16].”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, unknown): “This ’trick’ is nowadays known as the ’artificial viscosity switch’ [16, 15, 14].”
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems (2007, methodology): “First, by introducing formulations for multidimensional shock wave computations in [5] and then by using a discretization based on a mimetic finite difference scheme in [4].”
A new discretization methodology for diffusion problems on generalized polyhedral meshes (2007, methodology): “The methodology follows the general principle of the mimetic finite difference (MFD) method – to mimic the essential underlying properties of the original continuum differential operators such as the conservation laws, solution symmetries, and the fundamental identities and theorems of vector and te”
Mimetic finite difference method (2014, background): “…a magnetic diffusion, [148] [150]; equations of the Lagrangian hydrodynamics on general polygonal meshes, [66], including an artificial viscosity, [65]; equations of a solid dynamics and shallow water equations, [196]; and the Lagrangian hydrodynamics on curvilinear logically rectangular meshes…”