An a posteriori error estimator for the mimetic finite difference approximation of elliptic problems

By L. Beirão da Veiga, Gianmarco Manzini. 2008

53 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3789919870d37e590a82761cfc6aad6fa4190f9c

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A unified approach for handling convection terms in finite volumes and mimetic discretization methods for elliptic problems (2011, methodology): “In this framework, we mention, for instance, the Discontinuous Galerkin Method, [5, 44] and references therein, the Multi-Point Flux Approximation [1, 2, 48], the Mimetic Finite Difference Method, [8, 11–14,18, 20–23, 37, 40, 41] and references therein, the Hybrid Finite Volume Method [36], and the ”
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].”
Mimetic finite difference method (2014, methodology): “This post-processing method was successfully applied to develop a posteriori error estimators for the mimetic method described here and to implement adaptive mesh refinement strategies [22,31].”
A virtual element method with arbitrary regularity (2014, background): “…for mixed 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…”
New perspectives on polygonal and polyhedral finite element methods (2014, background): “A posteriori estimators for the mimetic discretizations appear in References [125, 126], and high-order mimetic discretizations are developed in References [127, 128, 129].”
Residual a posteriori error estimation for the Virtual Element Method for elliptic problems (2015, methodology): “In references [6, 8], the authors circumvent the absence of the shape functions by introducing a post-processed pressure solution that is used in the computation of the residual.”