A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation
Journal article, 2010
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 goal-oriented (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 (C) 2010 Elsevier B V All rights reserved
diffusion-reaction equation
linear-functional outputs
differential-equations
Flux-free error estimation
parabolic-problems
solutions
convergence-rates
computing bounds
adaptivity
poissons-equation
A posteriori error estimation
Finite element method
Stokes flow
exact weak
Asymptotic bounds
elasticity
Incompressible
Author
Fredrik Larsson
Chalmers, Applied Mechanics, Material and Computational Mechanics
P. Diez
Universitat Politecnica de Catalunya
A. Huerta
Universitat Politecnica de Catalunya
Computer Methods in Applied Mechanics and Engineering
0045-7825 (ISSN)
Vol. 199 37-40 2383-2402Subject Categories (SSIF 2011)
Mechanical Engineering
DOI
10.1016/j.cma.2010.03.011