TY - JOUR
T1 - Unified a Posteriori Error Estimator for Finite Element Methods for the Stokes Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 551
EP - 570
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/582.html
KW - A posteriori error estimate, finite element methods, Stokes equations.
AB - <p style="text-align: justify;">This paper is concerned with residual type a posteriori error estimators for finite
element methods for the Stokes equations. In particular, the authors established a unified approach for deriving and analyzing a posteriori error estimators for velocity-pressure based finite
element formulations for the Stokes equations. A general a posteriori error estimator was presented with a unified mathematical analysis for the general finite element formulation that covers
conforming, non-conforming, and discontinuous Galerkin methods as examples. The key behind
the mathematical analysis is the use of a lifting operator from discontinuous finite element spaces
to continuous ones for which all the terms involving jumps at interior edges disappear.</p>