A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh

Xiu Ye; Shangyou Zhang; Xiu Ye; Shangyou Zhang

doi:10.3934/era.2021053

Electronic Research Archive

2021, Volume 29, Issue 6: 3609-3627. doi: 10.3934/era.2021053

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A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh

Xiu Ye ^{1
,},
Shangyou Zhang ^{2
,
,}

1.
Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA
2.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

Received: 01 November 2020 Revised: 01 June 2021 Published: 22 July 2021
Primary: 65N15, 65N30, 76D07; Secondary: 35B45, 35J50

A stabilizer free WG method is introduced for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates two order higher than the optimal-order for velocity of the WG approximation is proved in both an energy norm and the $ L^2 $ norm. Optimal order error estimate for pressure in the $ L^2 $ norm is also established. The numerical examples cover low and high order approximations, and 2D and 3D cases.
- Weak Galerkin,
- finite element methods,
- the Stokes equations,
- superconvergence,
- polytopal mesh
Citation: Xiu Ye, Shangyou Zhang. A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh[J]. Electronic Research Archive, 2021, 29(6): 3609-3627. doi: 10.3934/era.2021053

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Abstract

A stabilizer free WG method is introduced for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates two order higher than the optimal-order for velocity of the WG approximation is proved in both an energy norm and the $ L^2 $ norm. Optimal order error estimate for pressure in the $ L^2 $ norm is also established. The numerical examples cover low and high order approximations, and 2D and 3D cases.

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