Electronic Research Archive

2021, 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

• 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.

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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• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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