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Generalized Weak Galerkin Methods For Stokes Equations

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arxiv 2205.10996 v1 pith:GRNV5ENQ submitted 2022-05-23 math.NA cs.NA

W. Qi (1) , P. Seshaiyer (2) , J. Wang (3) ((1) School of Mathematics , Information Sciences , Henan Normal University , (2) Department of Mathematical Sciences , George Mason University (3) Division of Mathematical Sciences , National Science Foundation) This is my paper · ORCID
classification math.NAcs.NA
keywords weakgalerkinnormequationsgeneralizedmethodstokesarbitrary
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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.

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