Domain decomposition methods for hp finite element approximations on anisotropic meshes

X. Vasseur, Seminar für Angewandte Mathematik, ETH Zürich

Monday, January 13
at 14.00
in HG E1.2

We present, certain Balancing Neumann-Neumann and one-level FETI domain decomposition methods for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes. These are meshes that are highly anisotropic where the aspect ratio grows exponentially with the polynomial degree. The condition number of the preconditioned operators is independent of the aspect ratio of the mesh and of potentially large jumps on the coefficients. In addition, it only grows poly logarithmically with the polynomial degree, as in the case of p approximations on shape-regular meshes. These features are illustrated by various numerical results on two- and three-dimensional applications.

This is a joint work with Dr, Andrea Toselli.