Multigrid method for noncoercive parabolic variational inequality
Abstract In this article, our work is focused on the proof of the uniform convergence of the multigrid method for parabolic variational inequality with a noncoercive operator and its numerical solution. To discretize the problem, we utilize a finite element scheme for the noncoercive operator and Eu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03285-8 |
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| Summary: | Abstract In this article, our work is focused on the proof of the uniform convergence of the multigrid method for parabolic variational inequality with a noncoercive operator and its numerical solution. To discretize the problem, we utilize a finite element scheme for the noncoercive operator and Euler scheme for the time. To obtain the system discretization of our problem, we reformulate the parabolic variational inequality as a Hamilton–Jacobi–Bellman equation. On the smooth grid, we apply the multigrid method as an interior iteration on the linear system. Finally, we provide a proof of the uniform convergence of the multigrid method for parabolic variational inequality with a noncoercive operator, providing a numerical example of this problem. |
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| ISSN: | 1029-242X |