Abstract
In this paper, we introduce a new method to analyze the convergence of the standard finite element method for elliptic variational inequalities with noncoercive operators (VI). The method consists of combining the so-called Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart, and then between the true solution and the approximate solution.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol22iss2pp114-119
- Journal
- Sultan Qaboos University Journal for Science, 22(2), 114
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Boulbrachene, M. (2018). Finite Element Approximation of Variational Inequalities: An Algorithmic Approach. Sultan Qaboos University Journal for Science, 22(2), 114. https://doi.org/10.24200/squjs.vol22iss2pp114-119
MLA 9
Boulbrachene, Messaoud. "Finite Element Approximation of Variational Inequalities: An Algorithmic Approach." Sultan Qaboos University Journal for Science, vol. 22, no. 2, 2018, pp. 114. https://doi.org/10.24200/squjs.vol22iss2pp114-119.
Chicago (author–date)
Boulbrachene, Messaoud. 2018. "Finite Element Approximation of Variational Inequalities: An Algorithmic Approach." Sultan Qaboos University Journal for Science 22 (2): 114. https://doi.org/10.24200/squjs.vol22iss2pp114-119.
Harvard
Boulbrachene, M. (2018) 'Finite Element Approximation of Variational Inequalities: An Algorithmic Approach', Sultan Qaboos University Journal for Science, 22(2), pp. 114. doi:10.24200/squjs.vol22iss2pp114-119.
Vancouver
Boulbrachene M. Finite Element Approximation of Variational Inequalities: An Algorithmic Approach. Sultan Qaboos University Journal for Science. 2018;22(2):114. doi:10.24200/squjs.vol22iss2pp114-119
IEEE
M. Boulbrachene, "Finite Element Approximation of Variational Inequalities: An Algorithmic Approach," Sultan Qaboos University Journal for Science, vol. 22, no. 2, pp. 114, 2018, doi: 10.24200/squjs.vol22iss2pp114-119.