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A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation
Larsson, Fredrik; Díez, Pedro; Huerta, Antonio
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation. Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly. The new estimator is built up by two key ingredients. At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems. Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error. In this manner, guaranteed upper and lower bounds, of the velocity “energy norm” of the error as well as goaloriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained. In particular, it should be noted that this approach requires no computation of hybrid fluxes. Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor– Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Finite element method
Error functions
Numerical analysis
Navier-Stokes equations
Elements finits, Mètode dels
Anàlisi numèrica
Equacions de Navier-Stokes
Attribution-NonCommercial-NoDerivs 3.0 Spain

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