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Pre-Publicación 2013-04

Tomás Barrios, Rommel Bustinza, Galina C. García, María González:

A posteriori error analyses of a velocity-pseudostress formulation of the generalized Stokes problem

Abstract:

We develop two a posteriori error analyses for an augmented mixed method for the generalized Stokes problem. The stabilized scheme is obtained by adding suitable least squares terms to the velocity-pseudostress formulation of the generalized Stokes problem. Then, in order to approximate its solution applying an adaptive mesh refinement technique, we derive two reliable a posteriori error estimators of residual type, and study their efficiency. To this aim, we include two different analyses: the standard residual based approach and an unusual one based on the Ritz projection of the error. The main difference of both approaches relies on the way we treat the nonhomogeneous boundary condition. Finally, we present some numerical examples that confirm the theoretical properties of our approach and estimators.

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