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Volume 33, Issue 3
A Modified Weak Galerkin Finite Element Method for Sobolev Equation

Fuzheng Gao & Xiaoshen Wang

DOI: 10.4208/jcm.1502-m4509

J. Comp. Math., 33 (2015), pp. 307-322.

Published online: 2015-06

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  • Abstract

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.

  • Keywords

Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak Galerkin, Error estimate.

  • AMS Subject Headings

65M15, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fzgao@sdu.edu.cn (Fuzheng Gao)

xxwang@ualr.edu (Xiaoshen Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-307, author = {Gao , Fuzheng and Wang , Xiaoshen}, title = {A Modified Weak Galerkin Finite Element Method for Sobolev Equation}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {3}, pages = {307--322}, abstract = {

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1502-m4509}, url = {http://global-sci.org/intro/article_detail/jcm/9844.html} }
TY - JOUR T1 - A Modified Weak Galerkin Finite Element Method for Sobolev Equation AU - Gao , Fuzheng AU - Wang , Xiaoshen JO - Journal of Computational Mathematics VL - 3 SP - 307 EP - 322 PY - 2015 DA - 2015/06 SN - 33 DO - http://doi.org/10.4208/jcm.1502-m4509 UR - https://global-sci.org/intro/article_detail/jcm/9844.html KW - Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak Galerkin, Error estimate. AB -

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.

Gao , Fuzheng and Wang , Xiaoshen. (2015). A Modified Weak Galerkin Finite Element Method for Sobolev Equation. Journal of Computational Mathematics. 33 (3). 307-322. doi:10.4208/jcm.1502-m4509
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