Non-mortar finite elements for elliptic problems

Vesselin Dobrev and Panayot S. Vassilevski

Central Laboratory for Parallel Processing, Bulgarian Academy of
Sciences,
Acad. G. Bonchev St., bl. 25 A, 1113, Sofia, Bulgaria

Based on a non-overlapping domain decomposition a non-mortar
finite element space is constructed that consists of a interface
space and arbitrary local (subdomain) spaces. A bounded, computable
extension mapping (from the interface to the subdomain interior)
is required for the stability of the discretization. Moreover,
in order to achieve certain discretization order the extension
mapping needs to be sufficiently smooth. Numerical experiments,
based on a discrete harmonic extension mapping, agree with  the
proven order of error estimates. The non-mortar finite element
discretization problems are naturally preconditioned by
a block diagonal preconditioner utilizing subdomain preconditioners
and a suitable interface preconditioner. The overall computational
process is suitable for parallel implementation as it is a
domain decomposition type method.