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Volume 32, Issue 2
On $L^2$ Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems

Fuzheng Gao & Lin Mu

DOI: 10.4208/jcm.1401-m4385

J. Comp. Math., 32 (2014), pp. 195-204.

Published online: 2014-04

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  • Abstract

A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in $L^2$ norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.

  • Keywords

WG-FEMs, discrete weak gradient, parabolic problem, error estimate.

  • AMS Subject Headings

65M15, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-195, author = {Fuzheng Gao and Lin Mu}, title = {On $L^2$ Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {2}, pages = {195--204}, abstract = {

A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in $L^2$ norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-m4385}, url = {http://global-sci.org/intro/article_detail/jcm/9878.html} }
TY - JOUR T1 - On $L^2$ Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems AU - Fuzheng Gao & Lin Mu JO - Journal of Computational Mathematics VL - 2 SP - 195 EP - 204 PY - 2014 DA - 2014/04 SN - 32 DO - http://doi.org/10.4208/jcm.1401-m4385 UR - https://global-sci.org/intro/article_detail/jcm/9878.html KW - WG-FEMs, discrete weak gradient, parabolic problem, error estimate. AB -

A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in $L^2$ norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.

Fuzheng Gao and Lin Mu. (2014). On $L^2$ Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems. Journal of Computational Mathematics. 32 (2). 195-204. doi:10.4208/jcm.1401-m4385
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