Multigrid method for noncoercive parabolic variational inequality

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.

• multigrid methods
• parabolic variational inequalities
• uniform convergence
• Hamilton-Jacobi-Bellman equation
• finite element discretization
• Euler scheme
• linear systems

• Advanced Numerical Methods in Computational Mathematics
• Nonlinear Partial Differential Equations
• Contact Mechanics and Variational Inequalities
• multigrid methods
• parabolic variational inequalities
• uniform convergence
• Hamilton-Jacobi-Bellman equation
• finite element discretization
• Euler scheme
• linear systems
• Computational Mechanics
• Applied Mathematics
• Computational Theory and Mathematics
• Engineering
• Mathematics
• Computer Science