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Volume 12, Issue 3
A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality

Hui Peng, Xiuli Wang, Qilong Zhai & Ran Zhang

DOI: 10.4208/nmtma.OA-2018-0124

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 923-941.

Published online: 2019-04

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  • Abstract

In this paper, we discuss the weak Galerkin (WG) finite element method for the obstacle problem and the second kind of the elliptic variational inequality. We use piecewise linear functions to approximate the exact solutions. The WG schemes for the first and the second kind of elliptic variational inequality are established and the well-posedness of the two schemes are proved. Furthermore, we can obtain the optimal order estimates in $H$1 norm. Finally, some numerical examples are presented to confirm the theoretical analysis.

  • Keywords

Obstacle problem, the second kind of elliptic variational inequality, weak Galerkin finite element method, discrete weak gradient.

  • AMS Subject Headings

65N30, 65N12, 35J85, 51M16, 26A27

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-923, author = {Hui Peng, Xiuli Wang, Qilong Zhai and Ran Zhang}, title = {A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {923--941}, abstract = {

In this paper, we discuss the weak Galerkin (WG) finite element method for the obstacle problem and the second kind of the elliptic variational inequality. We use piecewise linear functions to approximate the exact solutions. The WG schemes for the first and the second kind of elliptic variational inequality are established and the well-posedness of the two schemes are proved. Furthermore, we can obtain the optimal order estimates in $H$1 norm. Finally, some numerical examples are presented to confirm the theoretical analysis.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0124}, url = {http://global-sci.org/intro/article_detail/nmtma/13137.html} }
TY - JOUR T1 - A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality AU - Hui Peng, Xiuli Wang, Qilong Zhai & Ran Zhang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 923 EP - 941 PY - 2019 DA - 2019/04 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0124 UR - https://global-sci.org/intro/article_detail/nmtma/13137.html KW - Obstacle problem, the second kind of elliptic variational inequality, weak Galerkin finite element method, discrete weak gradient. AB -

In this paper, we discuss the weak Galerkin (WG) finite element method for the obstacle problem and the second kind of the elliptic variational inequality. We use piecewise linear functions to approximate the exact solutions. The WG schemes for the first and the second kind of elliptic variational inequality are established and the well-posedness of the two schemes are proved. Furthermore, we can obtain the optimal order estimates in $H$1 norm. Finally, some numerical examples are presented to confirm the theoretical analysis.

Hui Peng, Xiuli Wang, Qilong Zhai and Ran Zhang. (2019). A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 923-941. doi:10.4208/nmtma.OA-2018-0124
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