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

Ye, Xiu; Zhang, Shangyou

doi:10.3934/era.2021053

Cited by 15 publications

(1 citation statement)

References 19 publications

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“…This method is much more simpler than the standard WG‐FEMs with fewer coefficients and high orders of accuracy on polytopal/polyhedral meshes. SFWG finite element methods have been studied in [25–29] for elliptic problems and parabolic equation in [30].…”

Section: Introductionmentioning

confidence: 99%

A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation

Кумар

Deka

2022

Numerical Methods Partial

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In this study, we consider a stabilizer free weak Galerkin (SFWG) finite element method to solve a second‐order Sobolev equation. The SFWG method has various assets, including the support for higher order of accuracy and fewer coefficients. We have analyzed error estimates for both semidiscrete and fully discrete schemes using a non‐standard projection operator. The convergence rate of numerical error estimates of 0.3emO0.3em()hk+2+τ2$$ \kern0.3em O\kern0.3em \left({h}^{k+2}+{\tau}^2\right) $$ in L∞()H1$$ {L}^{\infty}\left({H}^1\right) $$ norm and 0.3emO0.3em()hk+3+τ2$$ \kern0.3em O\kern0.3em \left({h}^{k+3}+{\tau}^2\right) $$ in L∞()L2$$ {L}^{\infty}\left({L}^2\right) $$ norm are obtained, which are two order higher than the optimal order associated with WG finite element space ()ℙk(K),ℙk+1(∂K),[]ℙk+1(K)2.$$ \left({\mathrm{\mathbb{P}}}_k(K),{\mathrm{\mathbb{P}}}_{k+1}\left(\partial K\right),{\left[{\mathrm{\mathbb{P}}}_{k+1}(K)\right]}^2\right). $$ At last, several numerical examples are reported to validate the supercloseness property and efficiency of the proposed SFWG method. These experiments confirm the accuracy of the theoretical findings.

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Section: Introductionmentioning

confidence: 99%

A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation

Кумар

Deka

2022

Numerical Methods Partial

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A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes

Zhang

2021

Numerical Methods in Fluids

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A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity‐pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general polygonal/polyhedral meshes. Most finite element methods with discontinuous approximation have one or more stabilizing terms for velocity and for pressure to guarantee stability and convergence. This new finite element method has the standard conforming finite element formulation, without any velocity or pressure stabilizers. Optimal‐order error estimates are established for the corresponding numerical approximation in various norms. The numerical examples are tested for low and high order elements up to the degree four in 2D and 3D spaces.

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Superconvergent P1 honeycomb virtual elements and lifted P3 solutions

Lin,

Xu,

Zhang

2024

Calcolo

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

Cited by 15 publications

References 19 publications

A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation

A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation

A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes

Superconvergent P1 honeycomb virtual elements and lifted P3 solutions

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