A systematic study on weak Galerkin finite element method for second‐order parabolic problems
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 solutio...
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| Veröffentlicht in: | Numerical methods for partial differential equations Jg. 39; H. 3; S. 2444 - 2474 |
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Hoboken, USA
John Wiley & Sons, Inc
01.05.2023
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| Abstract | 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 𝒫k(K),𝒫j(∂K),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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| AbstractList | 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 ð'«k(K),ð'«j(∂K),ð'«l(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. 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 𝒫k(K),𝒫j(∂K),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. 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 and norms for a general WG element , where , and 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. |
| Author | Kumar, Naresh Deka, Bhupen |
| Author_xml | – sequence: 1 givenname: Bhupen orcidid: 0000-0003-2193-063X surname: Deka fullname: Deka, Bhupen email: bdeka@iitg.ac.in organization: Indian Institute of Technology Guwahati – sequence: 2 givenname: Naresh orcidid: 0000-0002-1913-7950 surname: Kumar fullname: Kumar, Naresh organization: Indian Institute of Technology Guwahati |
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| SubjectTerms | convergence analysis discrete weak gradient Finite element method Galerkin method Norms parabolic problems Polynomials Robustness (mathematics) semidiscrete and fully discrete schemes weak Galerkin finite element method |
| Title | A systematic study on weak Galerkin finite element method for second‐order parabolic problems |
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