A Posteriori Error Analysis And An Adaptive Strategy For A Generalized Stokes Problem.

Abstract

In this work we propose a new a posteriori error estimator for the Stokes problem,
both with and without a reaction term. This 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.