A Posteriori Error Estimate for Stabilized Finite Element Methods for the Stokes Equations

Abstract

Computation with adaptive grid refinement has proved to be a useful and efficient tool in scientific computing over the last several decades. The key behind this technique is the design of a good a posterior error estimator that provides a guidance on how and where grids should be refined. In this paper, the authors propose and analyze a posteriori error estimator for a stabilized finite element method in computational fluid dynamics. The main contributions of the paper are: (1) an efficient a posteriori error estimator is designed and analyzed for a general stabilized finite element method, (2) a rigorous mathematical analysis is established for a theoretical justification of its efficiency and generality to other applications, and (3) some computational results with a comparison with other methods are presented for a computational justification of the proposed a posteriori error estimator.