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Keywords:

  • inf-sup condition;
  • L2 projection method;
  • stabilized finite element method;
  • Stokes equations;
  • superconvergence

Abstract

This article first recalls the results of a stabilized finite element method based on a local Gauss integration method for the stationary Stokes equations approximated by low equal-order elements that do not satisfy the inf-sup condition. Then, we derive general superconvergence results for this stabilized method by using a local coarse mesh L2 projection. These supervergence results have three prominent features. First, they are based on a multiscale method defined for any quasi-uniform mesh. Second, they are derived on the basis of a large sparse, symmetric positive-definite system of linear equations for the solution of the stationary Stokes problem. Third, the finite elements used fail to satisfy the inf-sup condition. This article combines the merits of the new stabilized method with that of the L2 projection method. This projection method is of practical importance in scientific computation. Finally, a series of numerical experiments are presented to check the theoretical results obtained. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 115-126, 2012