Problèmes mathématiques de la mécanique/Mathematical Problems in Mechanics On a Residual Local Projection Method for the Darcy Equation

(Reçu le, accepte ́ le) Abstract. A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions of residual dependent local Darcy prob-lems obtained after a static condensation procedure. We prove the method achieves error optimality and indicates a way to recover a locally mass conservative velocity field. Numer-ical experiments validate theory. c © 2009 Académie des sciences / ´Editions scientifiques et médicales Elsevier SAS Une Méthode de Projection Local Résiduelle pour l ’ ´Equation de Darcy Note présentée par S0764-4442(00)0????-?/FLA c © 2009 Académie des sciences / ´Editions scientifiques et médicales Elsevier SAS. Tous droits réservés.