A Two-Grids/Projection Algorithm for Obstacle Problems

In order to emphasize the possible relation between discontinuous and continuous approximations on different meshes, a two-grids method for the resolution of parabolic variational inequality problems is presented. The numerical methodology combines a time splitting algorithm to decouple a diffusion phenomenon from an obstacle problem. The diffusion problem is solved by using finite differences, while piecewise linear finite element techniques are used together with a Newton method for the obstacle problem. Projections are used to interpolate the solution from one grid to the other. Numerical experiments show that the resulting method has good accuracy properties.