Publication

Estimation d'erreur d'une méthode de volumes-éléments finis stabilisée appliquée au problème de Stokes stationnaire et transient

2009
Student Projects

Abstract

The present report addresses the rigorous study of convergence of a stabilized finite volume element method applied to stationary and time dependent Stokes problems. Some preliminary results about the existence and uniqueness of solution at continuous and discrete level are provided for stabilized finite element and finite volume element formulations when using two different stabilization techniques, and then we prove consistency of the methods for the time-independent and time-dependent problems, and derive optimal convergence rates.

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2009
Student Projects

Abstract

Official source

Related concepts (27)

Consistency

In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Equiconsistency

In mathematical logic, two theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and vice versa. In this case, they are, roughly speaking, "as consistent as each other". In general, it is not possible to prove the absolute consistency of a theory T. Instead we usually take a theory S, believed to be consistent, and try to prove the weaker statement that if S is consistent then T must also be consistent—if we can do this we say that T is consistent relative to S.

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Estimation d'erreur d'une méthode de volumes-éléments finis stabilisée appliquée au problème de Stokes stationnaire et transient

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