Singularities and Error Estimates in

Violaine Maugain

Description

Niveau: Supérieur, Doctorat, Bac+8
Singularities and Error Estimates in Non-Conforming Approximation of Two-Dimensional Diusion Problem P. Lesaint V. Louvet y Abstract The solution of a two dimensional diusion problem with discontinuous coef- cients is analyzed on a particular two-regions domain. The solution is shown to contain a singular part, and the particular behavior is quantitatively evaluated. It is well kown that the degree of regularity of the solution for such problem deter- mines the accuracy of the numerical techniques used to approximate the solution. The presence of singular points will then aect the convergence orders for numerical solution of the problem. This consequences are analyzed by deriving some error estimates for a non-conforming approximation. The real eects of the singularity are then studied on numerical calculations for dierent non-conforming elements. We will conclude from these tests that the damages due to the singularity are not as many important as theory may provided. Rsum On etudie dans ce travail un probleme de diusion a coecients discontinus dans le cas particulier d'un domaine compose de deux regions distinctes. La so- lution contient alors une partie singuliere que nous evaluons en etudiant la forme analytique du ux aux points singuliers. Sachant que le degre de regularite de la fonction joue un ro^le primordial sur la precision des methodes numeriques uti- lisees, nous etudions l'impact des singularites sur les majorations d'erreur d'une approximation non conforme.

• ux aux points singuliers


• singular point


• problem


• zero ux boundary


• fast methods


• impact des singularites sur les majorations d'erreur

Sujets

• Problem

Informations

• Publié par: mijec
• Nombre de lectures: 20
• Langue: English

Extrait

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