Multigrid method for noncoercive parabolic variational inequality

Abstract

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.

Keywords

• Multigrid method
• Parabolic variational inequality
• Noncoersive operator
• Hamilton–Jacobi–Bellman equation
• Numerical methods