Optimal extensions on tensor-product meshes (Q2486137)

This paper is dedicated to the development of fast solvers for the linear system arising from the discretization by the \(p\)-version of the finite element method of a uniformly elliptic second-order boundary value problem. In this way, the authors analyze an inexact Dirichlet-Dirichlet domain decomposition preconditioner, which uses as a basic ingredient an extension operator. Beyond a careful study of mathematical convergence, the proposed method is illustrated by two convincing numerical examples. Moreover, the paper is nicely written.