A Near-Optimal Hierarchical Estimate Based Adaptive Finite Element Method for Obstacle Problems

摘要

Adaptive solvers are now widely used in numerical simulations of lots of problems for better accuracy with minimal computational cost. The reasons for choosing adaptive method for the problem (1) are two-folded. First, the grid in the contact zone is often not necessarily as fine as that in the non-contact zone. Secondly, the solution u may have singularity in some local areas. Therefore, for obstacle problems, a finite element solution on a suitable non-uniform grid may approximate the exact solution much better than that on a uniform grid with the same number of degrees of freedoms. Solvers which can generate non-uniform grids adaptively according to the problem to-be-solved are desired.