Title: Analysis of two-dimensional FETI-DP preconditioners by the
standard additive Schwarz framework
Authors: Susanne C. Brenner
Status: to appear in Electronic Transactions on Numerical Analysis (ETNA)
Abstract: FETI-DP preconditioners for two-dimensional elliptic boundary
value problems with heterogeneous coefficients are analyzed by
the standard additive Schwarz framework. It is shown that the
conditional number of the preconditioned system for both second
order and fourth order problems is bounded by C(1+ln(H/h))^2,
where H is the maximum of the diameters of the subdomains, h is
the mesh size of a quasi-uniform triangulation, and the positive
constant C is independent of h, H, the number of subdomains and
the coefficients of the boundary value problems on the subdomains.
The sharpness of the bound for second order problems is also
established.