Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations

Raviart, Pierre Arnaud; Thomas, Jean-Marie

doi:10.2307/2006423

Cited by 111 publications

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“…Problem (8) is a particular case of the general hybrid formulation proposed in [4]. Therefore, this result follows, as in [4], from the proof of Theorem 1 in [8].…”

Section: The Hybrid Formulationsupporting

confidence: 52%

A Locking-Free MHM Method for Elasticity

Pereira¹,

Valentin²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. This work presents a multiscale hybrid-mixed finite element (MHM) method for the two-and three-dimensional linear elasticity problem that deals with nearly incompressible and heterogeneous isotropic materials. The starting point is a dual-hybrid form of the elasticity model defined on a coarse mesh, which is equivalent to a set of element-wise elasticity problems brought together by a face-based global formulation. Importantly, the local problems are independent to one another and determine the basis functions. Thereby, the basis naturally incorporate multiscale features of the media. This new variant of the MHM method turns out to be robust in the incompressible limit case as a result of the use of a stabilized finite element method to approximate basis functions. Some preliminary theoretical results are addressed.

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“…Problem (8) is a particular case of the general hybrid formulation proposed in [4]. Therefore, this result follows, as in [4], from the proof of Theorem 1 in [8].…”

Section: The Hybrid Formulationsupporting

confidence: 52%

A Locking-Free MHM Method for Elasticity

Pereira¹,

Valentin²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…The global action guarantees that the local functions are correctly glued together, see the characterization (2.12) of H 1 0 (Ω) in Raviart and Thomas [13].…”

Section: (W(x) − W(y)) (V(x) − V(y))mentioning

confidence: 95%

“…As far as we know, the use of the space X δ was introduced by Raviart and Thomas [13] and X was considered by Braess, Dahmen and Wieners [2] and by Ben Belgacem [3]. Following their analysis, one sees that H 1 0 (Ω) can be identify as a subspace of X and, also, as a subspace of X δ by means of appropriate linear restrictions:…”

Section: (W(x) − W(y)) (V(x) − V(y))mentioning

confidence: 99%

Stabilization of a non standard FETI-DP mortar method for the Stokes problem

Vera

Rebollo

2014

ESAIM: M2AN

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Abstract. In a recent paper [E. Chacón Vera and D. Franco Coronil, J. Numer. Math. 20 (2012) 161-182.] a non standard mortar method for incompressible Stokes problem was introduced where the use of the trace spaces H 1/2 and H 1/2 00 and a direct computation of the pairing of the trace spaces with their duals are the main ingredients. The importance of the reduction of the number of degrees of freedom leads naturally to consider the stabilized version and this is the results we present in this work. We prove that the standard Brezzi-Pitkaranta stabilization technique is available and that it works well with this mortar method. Finally, we present some numerical tests to illustrate this behaviour.Mathematics Subject Classification. 65N30, 65N55.

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“…Let Π h denote the usual Raviart-Thomas projection, which has the following properties [1,3,22,23,27] (…”

Section: Error Estimatesmentioning

confidence: 99%

Mixed finite element-based fully conservative methods for simulating wormhole propagation

Kou

Sun

2016

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. MIXED FINITE ELEMENT-BASED FULLY CONSERVATIVE METHODS FOR SIMULATING WORMHOLE PROPAGATION *JISHENG KOU † , SHUYU SUN ‡ , AND YUANQING WU § Abstract. Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy-Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy-Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

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Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations

Cited by 111 publications

References 0 publications

A Locking-Free MHM Method for Elasticity

A Locking-Free MHM Method for Elasticity

Stabilization of a non standard FETI-DP mortar method for the Stokes problem

Mixed finite element-based fully conservative methods for simulating wormhole propagation

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