Computer Methods in Applied Mechanics and Engineering
A posteriori error estimates for the Stokes problem
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Error estimators for nonconforming finite element approximations of the Stokes problem
Mathematics of Computation
A Posteriori Error Estimators for the Stokes and Oseen Equations
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations
SIAM Journal on Scientific Computing
An adaptive stabilized finite element scheme for the advection-reaction-diffusion equation
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem
SIAM Journal on Numerical Analysis
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Stable and unstable cross-grid PkQl mixed finite elements for the Stokes problem
Journal of Computational and Applied Mathematics
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In this work we present an adaptive strategy (based on an a posteriori error estimator) for a stabilized finite element method for the Stokes problem, with and without a reaction term. The hierarchical type estimator is based on the solution of local problems posed on appropriate finite dimensional spaces of bubble-like functions. An equivalence result between the norm of the finite element error and the estimator is given, where the dependence of the constants on the physics of the problem is explicited. Several numerical results confirming both the theoretical results and the good performance of the estimator are given.