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A NEW HYBRIDIZED MIXED weak GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC PROBLEMS

Journal of Computational Mathematics 2022年第4期40卷 499-516页

作者： Abdelhamid Zaghdani Sayed Sayari Miled EL Hajji University of Tunis Boulevard du 9 avril 1939 TunisDepartment of MathematicsEnsitTaha Hussein AvenueMontfleuryTunisTunisia Northern Border University Faculty of Arts and ScienceRafhaP.O.840Saudi Arabia Carthage University Isteub2 Rue de l’Artisanat Charguia 22035 TunisTunisia Department of Mathematics Faculty of SciencesUniversity of JeddahSaudi Arabia ENIT-LAMSINBP.371002 Tunis-Belv´ed`ereTunis El Manar UniversityTunisia

In this paper,a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic *** method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element *** discrete inequalities are presented on discontinuous spaces and optimal order error estimations are *** numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method.

关键词： weak Galerkin weak gradient Hybridized mixed finite element method Second order elliptic problems

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A hybridized weak Galerkin finite element scheme for the Stokes equations

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Science China Mathematics 2015年第11期58卷 2455-2472页

作者： ZHAI QiLong ZHANG Ran WANG XiaoShen Department of Mathematics Jilin University Department of Mathematics University of Arkansas at Little Rock

In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is *** WG method uses weak functions and their weak derivatives which are defined as *** functions and weak derivatives can be approximated by piecewise polynomials with various *** combination of polynomial spaces leads to different WG finite element methods,which makes WG methods highly flexible and efficient in practical computation.A Lagrange multiplier is introduced to provide a numerical approximation for certain derivatives of the exact *** this new feature,the HWG method can be used to deal with jumps of the functions and their flux *** order error estimates are established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multiplier.A Schur complement formulation of the HWG method is derived for implementation *** validity of the theoretical results is demonstrated in numerical tests.

关键词： hybridized weak Galerkin finite element methods weak gradient weak divergence Stokes equation

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A weak Galerkin-mixed finite element method for the Stokes-Darcy problem

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Science China Mathematics 2021年第10期64卷 2357-2380页

作者： Hui Peng Qilong Zhai Ran Zhang Shangyou Zhang School of Mathematics Jilin UniversityChangchun 130012China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface *** use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also *** experiments validate the theoretical analysis.

关键词： weak Galerkin finite element methods mixed finite element methods weak gradient coupled Stokes-Darcy problems

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A Discontinuous Galerkin Finite Element Method without Interior Penalty Terms

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 299-314页

作者： Fuzheng Gao Xiu Ye Shangyou Zhang School of Mathematics Shandong UniversityJinanShandong 250100China Department of Mathematics University of Arkansasat Little RockLittle RockAR 72204USA Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

A conforming discontinuous Galerkinﬁnite element method was introduced by Ye and Zhang,on simplicial meshes and on polytopal meshes,which has theﬂexibility of using discontinuous approximation and an ultra simple *** main goal of this paper is to improve the above discontinuous Galerkinﬁnite element method so that it can handle nonhomogeneous Dirichlet boundary conditions *** addition,the method has been generalized in terms of approximation of the weak *** estimates of optimal order are established for the correspond-ing discontinuousﬁnite element approximation in both a discrete H1 norm and the L2 *** results are presented to conﬁrm the theory.

关键词： Nonhomogeneous Dirichlet boundary conditions weak gradient discontinuous Galerkin stabilizer penalty free finite element methods polytopal mesh

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