A numerical study on Neumann-Neumann and FETI methods for hp approximations on geometrically refined boundary layer meshes in two dimensions

Abstract

We present extensive numerical tests showing the performance and robustness of certain Balancing Neumann–Neumann and one-level FETI methods for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in two dimensions. The numerical results confirm the theoretical results derived in [A. Toselli, X. Vasseur, Technical Report 02-15, Seminar für Angewandte Mathematik, ETH, Zürich, September 2002]: the condition numbers are independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients. In addition, they only grow polylogarithmically with the polynomial degree, as in the case of p approximations on shape-regular meshes.