A globally divergence-free weak Galerkin method for Brinkman equations

Zhang, Li; Feng, Meiqiang; Zhang, Jian

doi:10.1016/j.apnum.2018.11.002

Cited by 8 publications

(2 citation statements)

References 95 publications

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“…The concept of weak derivatives makes WG a widely applicable numerical technique for a large variety of PDEs arising from the mathematical modeling of practical problems in science and engineering. There is abundant existing literature on such PDEs; for example, elliptic equation [3][4][5][6][7][8][9][10], parabolic equation [11][12][13][14], system of equations [15][16][17][18][19][20][21][22][23], interface problems [24][25][26]. One close relative of the WG finite element method is the hybridizable discontinuous Galerkin (HDG) method [27].…”

Section: Introductionmentioning

confidence: 99%

A systematic study on weak Galerkin finite element method for second‐order parabolic problems

Deka

Кумар

2022

Numerical Methods Partial

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In the present work, we have described a systematic numerical study on weak Galerkin (WG) finite element method for second‐order linear parabolic problems by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in L∞()L2$$ {L}^{\infty}\left({L}^2\right) $$ and L∞()H1$$ {L}^{\infty}\left({H}^1\right) $$ norms for a general WG element 𝒫kfalse(Kfalse),𝒫jfalse(∂Kfalse),[]𝒫l(K)2, where k≥1$$ k\ge 1 $$, j≥0$$ j\ge 0 $$ and l≥0$$ l\ge 0 $$ are arbitrary integers. The fully discrete space–time discretization is based on a first order in time Euler scheme. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.

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Section: Introductionmentioning

confidence: 99%

A systematic study on weak Galerkin finite element method for second‐order parabolic problems

Deka

Кумар

2022

Numerical Methods Partial

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“…The concept of weak derivatives makes WG a widely applicable numerical technique for a large variety of of PDEs arising from the mathematical modeling of practical problems in science and engineering. There is an abundant literature on such PDEs; see, e.g., elliptic equation [18,20,21,22,27,36,37,39], parabolic equation [19,42,43,45], system of equations [23,25,26,28,29,31,35,40,44], interface problems [17,30,32]. One close relative of the WG finite element method is the hybridizable discontinuous Galerkin (HDG) method [10].…”

Section: Introductionmentioning

confidence: 99%

A Systematic Study on Weak Galerkin Finite Element Method for Second Order Parabolic Problems

Deka¹,

Kumar²

2021

Preprint

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A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in L ∞ (L 2 ) and L ∞ (H 1 ) norms for a general WG element (P k (K), Pj(∂K), P l (K)2 ), where k ≥ 1, j ≥ 0 and l ≥ 0 are arbitrary integers. The fully discrete space-time discretization is based on a first order in time Euler scheme. Our results are intended to extend the numerical analysis of WG methods for elliptic problems [J. Sci. Comput., 74 (2018), 1369-1396 to parabolic problems. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.

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Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions

Deka

Кумар

2021

Applied Numerical Mathematics

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A globally divergence-free weak Galerkin method for Brinkman equations

Cited by 8 publications

References 95 publications

A systematic study on weak Galerkin finite element method for second‐order parabolic problems

A systematic study on weak Galerkin finite element method for second‐order parabolic problems

A Systematic Study on Weak Galerkin Finite Element Method for Second Order Parabolic Problems

Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions

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