A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality

A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0124

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 923–941

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

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

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