caa a22 4500 378847821 CHVBK 20180305123316.0 cr unu---uuuuu 161128e20030601xx s 000 0 eng 10.1515/156939803322380800 doi (NATIONALLICENCE)gruyter-10.1515/156939803322380800 Akimov V.V. ∗ University of Jyäskylä, Department of Mathematical Information Technology, FIN-40351 Jyväskylä, Finland Additive Schwarz preconditioner for the Neumann problem with a boundary layer [Elektronische Daten] [V.V. Akimov] In this paper we consider a variant of the additive Schwarz preconditioner for elliptic finite element problems on meshes which are strongly refined in the vicinity of the Neumann boundary condition. Local refinements can be motivated by a sharp boundary layer in the solution of the underlying differential equation or they may occur in a method for solving another differential problem. The classical example of the latter situation is the L 2-projection (or the splitting-up) method for the Navier-Stokes equations. For a model problem we introduce an additive Schwarz preconditioner and prove that the condition number of the preconditioned stiffness matrix is bounded from above by a constant which is independent of the mesh and the width of the boundary layer. We consider several generalizations and applications of the results to the model problem. In particular, we discuss the application of the proposed preconditioner in the mortar element method. Numerical computations confirm the theoretical results of the paper. Copyright 2003, Walter de Gruyter Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 185-206 0927-6467 18:3<185 2003 18 rnam https://doi.org/10.1515/156939803322380800 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939803322380800 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Akimov V.V. ∗ University of Jyäskylä, Department of Mathematical Information Technology, FIN-40351 Jyväskylä, Finland NATIONALLICENCE 773 0- Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 185-206 0927-6467 18:3<185 2003 18 rnam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter