Consistent and mimetic discretizations in general relativity [PDF]
Journal of Mathematical Physics, 2004 A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level.
Arnowitt R. +3 more
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A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems [PDF]
Computers & Mathematics with Applications, 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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Elementary dispersion analysis of some mimetic discretizations on triangular C-grids [PDF]
Journal of Computational Physics, 2017 Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid ...
Danilov, Sergey, Korn, Peter
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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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On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study [PDF]
, 2016 It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the ...
Antonietti, Paola F. +3 more
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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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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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A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods [PDF]
, 2008 We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids.
Eymard R. +4 more
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Mixed Mimetic Spectral Element method applied to Darcy's problem
, 2013 We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relations.
Gerritsma, Marc +2 more
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Virtual Element Methods for hyperbolic problems on polygonal meshes [PDF]
, 2016 In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence estimates in H^1 semi-
Vacca, Giuseppe
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