Optimal extensions on tensor-product meshes Original Research Article

In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet–Dirichlet domain decomposition preconditioner for the system of linear algebraic equations is investigated. The ingredients of such a preconditioner are a preconditioner for the Schur complement, a preconditioner for the subdomains and an extension operator operating from the edges of the elements into their interior. Using methods of multi-resolution analysis, we propose a new method in order to compute the extension efficiently. Numerical experiments show the optimal performance of the described extension.