Superconvergence of a stabilized finite element approximation for the Stokes equations using a local coarse mesh L2 projection

Release Time:2025-04-30  Hits:

• Date:2025-04-30
• Title of Paper:Superconvergence of a stabilized finite element approximation for the Stokes equations using a local coarse mesh L2 projection
• Journal:Numerical methods for PDEs
• Summary: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.
• Co-author:Jian Li, Liquan Mei, Zhangxin Chen
• Volume:28(1)
• Page Number:115-126
• Translation or Not:No
• Date of Publication:2012-01-16