Two-level Schwarz methods for Wilson element approximation of elasticity problem Original Research Article

In this paper, a two-level additive and multiplicative Schwarz methods are developed for the Wilson nonconforming element approximation of elasticity problem. A new intergrid operator for the Wilson element is constructed. It is well known that the two-level additive Schwarz method can be seen as a preconditioning system, so the condition number of the preconditioning system for elasticity problem is proved to be bounded by a constant independent of mesh size and the number of subdomains. For the multiplicative method, the optimal rate of convergence is also obtained.