A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations

Authors:
Javier de Frutos;Bosco García-Archilla;Julia Novo
Affiliations:
Departamento de Matemática Aplicada, Universidad de Valladolid, Spain;Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain;Departamento de Matemáticas, Universidad Autónoma de Madrid, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the error in a steady Stokes problem. As a consequence, any available procedure to estimate the error in a Stokes problem can be used to estimate the error in the nonlinear evolutionary problem. A practical procedure to estimate the error based on the so-called postprocessed approximation is also considered. Both the semidiscrete (in space) and the fully discrete cases are analyzed. Some numerical experiments are provided.