An overlapping domain decomposition preconditioner for an anisotropic h-adaptive finite element method Original Research Article

A domain decomposition preconditioner for an anisotropic h-adaptive finite element method is proposed. The method is a version of the approach proposed by M. Dryja and O. Widlund. An effective and flexible algorithm to decompose an h-adaptive mesh into subdomains with the user controlled size is proposed. The analysis of the preconditioner applied to discretizations with constrained elements and with elements significantly stretched in one direction is presented. It shows that the condition number of the preconditioned system is independent of the finite element discretization. The preconditioner is suited for parallel computations. A number of representative tests with uniform and h-adaptive meshes illustrate the performance of the preconditioner.