Generalized Weak Galerkin Methods For Stokes Equations

W. Qi; P. Seshaiyer; J. Wang

Generalized Weak Galerkin Methods For Stokes Equations

Numerical Analysis 2022-05-24 v1 Numerical Analysis

Authors: W. Qi , P. Seshaiyer , J. Wang

Abstract

A new weak Galerkin finite element method, called generalized weak Galerkin method ({g}WG), is introduced for Stokes equations in this paper by using a new definition of the weak gradient. Error estimates in energy norm and $L^2$ norm for the velocity and $L^2$ norm for the pressure are derived for elements with arbitrary combination of polynomials. Some numerical examples are presented to verify the effectiveness, theoretical convergence orders, and robustness of the proposed scheme.

Keywords

weak galerkin finite element methods galerkin methods weak solutions

Cite

@article{arxiv.2205.10996,
  title  = {Generalized Weak Galerkin Methods For Stokes Equations},
  author = {W. Qi and P. Seshaiyer and J. Wang},
  journal= {arXiv preprint arXiv:2205.10996},
  year   = {2022}
}

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