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 ...
Cameron Talischi, G. Paulino
semanticscholar +4 more sources
A finite element framework for some mimetic finite difference discretizations
Computers & Mathematics with Applications, 2015 submitted
Rodrigo, Carmen +3 more
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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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Selecciones Matemáticas, 2021 Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since ...
Abdul Abner Lugo Jiménez +2 more
semanticscholar +1 more source
Mimetic finite difference methods in image processing [PDF]
Computational & Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bazan, C. +3 more
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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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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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Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence [PDF]
Computers & Fluids, 2020 This work studies the parallelization and empirical convergence of two finite difference acoustic wave propagation methods on 2-D rectangular grids, that use the same alternating direction implicit (ADI) time integration. This ADI integration is based on
Beatriz Otero +3 more
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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
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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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