Skip to main content
    • Aa
    • Aa

A Posteriori Error Estimator for a Weak Galerkin Finite Element Solution of the Stokes Problem

  • Xiaobo Zheng (a1) and Xiaoping Xie (a1)

A robust residual-based a posteriori error estimator is proposed for a weak Galerkin finite element method for the Stokes problem in two and three dimensions. The estimator consists of two terms, where the first term characterises the difference between the L 2-projection of the velocity approximation on the element interfaces and the corresponding numerical trace, and the second is related to the jump of the velocity approximation between the adjacent elements. We show that the estimator is reliable and efficient through two estimates of global upper and global lower bounds, up to two data oscillation terms caused by the source term and the nonhomogeneous Dirichlet boundary condition. The estimator is also robust in the sense that the constant factors in the upper and lower bounds are independent of the viscosity coefficient. Numerical results are provided to verify the theoretical results.

Corresponding author
*Corresponding author. Email addresses: (X. Zheng), (X. Xie)
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 2
Total number of PDF views: 11 *
Loading metrics...

Abstract views

Total abstract views: 60 *
Loading metrics...

* Views captured on Cambridge Core between 7th September 2017 - 19th October 2017. This data will be updated every 24 hours.