Publication: A numerical solution of parabolic quasi-variational inequality nonlinear using Newton-multigrid method
Date
2024
Authors
Bahi M.
Beggas M.
Nesba N.
Imtiaz A.
Journal Title
Journal ISSN
Volume Title
Publisher
Ferdowsi University of Mashhad
Abstract
In this article, we apply three numerical methods to study the L�convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand side. To discretize the problem, we utilize a finite element method for the operator and Euler scheme for the time. To obtain the system discretization of the problem, we reformulate the parabolic quasi-variational inequality as a Hamilton?Jacobi?Bellman equation. For linearizing the problem on the coarse grid, we employ Newton?s method as an external interior iteration of the Jacobian system. On the smooth grid, we apply the multigrid method as an interior iteration on the Jacobian system. Finally, we provide a proof for the L�-convergence of the Newton-multigrid method for parabolic quasi-variational inequalities with a nonlinear right-hand, by giving a numerical example for this problem. ? 2024 Ferdowsi University of Mashhad. All rights reserved.