A conforming discontinuous Galerkin finite element method for Brinkman equations

被引：2

作者：

Dang, Haoning ^{[1
]}

Zhai, Qilong ^{[1
]}

Zhao, Zhongshu ^{[2
,3
]}

机构：

[1] Jilin Univ, Sch Math, Changchun, Peoples R China

[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China

[3] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 440卷

基金：

中国国家自然科学基金;

关键词：

Brinkman equations; Discontinuous Galerkin; Discrete weak gradient operators; Polygonal meshes; STOKES;

D O I：

10.1016/j.cam.2023.115619

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a conforming discontinuous Galerkin (CDG) finite element method for Brinkman equations. The velocity stabilizer is removed by employing the higher degree polynomials to compute the weak gradient. The theoretical analysis shows that the CDG method is actually stable and accurate for the Brinkman equations. Optimal order error estimates are established in H-1 and L-2 norm. Finally, numerical experiments verify the stability and accuracy of the CDG numerical scheme.

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页数：16

相关论文

共 31 条

[1] A note on the optimal degree of the weak gradient of the stabilizer free weak Galerkin finite element method [J].

Al-Taweel, Ahmed ;

Wang, Xiaoshen .

APPLIED NUMERICAL MATHEMATICS, 2020, 150 :444-451

[2] An augmented velocity-vorticity-pressure formulation for the Brinkman equations [J].

Anaya, Veronica ;

Gatica, Gabriel N. ;

Mora, David ;

Ruiz-Baier, Ricardo .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2015, 79 (03) :109-137

[3] Darcy-Brinkman-Forchheimer Model for Film Boiling in Porous Media [J].

Avramenko, A. A. ;

Shevchuk, Igor, V ;

Kovetskaya, M. M. ;

Kovetska, Y. Y. .

TRANSPORT IN POROUS MEDIA, 2020, 134 (03) :503-536

[4] UNIFIED STABILIZED FINITE ELEMENT FORMULATIONS FOR THE STOKES AND THE DARCY PROBLEMS [J].

Badia, Santiago ;

Codina, Ramon .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) :1971-2000

[5]

BRINKMAN HC, 1947, APPL SCI RES, V1, P27

[6] A mixed virtual element method for the Brinkman problem [J].

Caceres, Ernesto ;

Gatica, Gabriel N. ;

Sequeira, Filander A. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017, 27 (04) :707-743

[7] A note on discontinuous galerkin divergence-free solutions of the navier-stokes equations [J].

Cockburn, Bernardo ;

Kanschat, Guido ;

Schotzau, Dominik .

JOURNAL OF SCIENTIFIC COMPUTING, 2007, 31 (1-2) :61-73

[8] A FINITE ELEMENT METHOD BASED ON WEIGHTED INTERIOR PENALTIES FOR HETEROGENEOUS INCOMPRESSIBLE FLOWS [J].

D'Angelo, Carlo ;

Zunino, Paolo .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (05) :3990-4020

[9] Brinkman equation in reactive flow: Contribution of each term in carbonate acidification simulations [J].

Ferreira, Leandro de Paulo ;

Oliveira, Thomas David Serafini de ;

Surmas, Rodrigo ;

Silva, Monica Antunes Pereira da ;

Pecanha, Ricardo Pires .

ADVANCES IN WATER RESOURCES, 2020, 144

[10] Investigation of the effective permeability of vuggy or fractured porous media from a Darcy-Brinkman approach [J].

Golfier, F. ;

Lasseux, D. ;

Quintard, M. .

COMPUTATIONAL GEOSCIENCES, 2015, 19 (01) :63-78

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