A fast solving method for elliptic problems in domains with re-entrant corners

Abstract

A fast method (MFMA) for solution of the Poisson equation −∆u = f with homogeneous Dirichlet boundary conditions in a unit sector with an angle α, α > π, is proposed. As a result of application of MFMA under the condition f ∈ W n 2 (Ω), the solution accuracy of the order O(n| ln h|h n+1 ) in the energy norm is achieved requiring O(n 2 h −2 ) operations.where f ∈ W n 2 (Ω), n is a natural number.