The boundary element method with Lagrangian multipliers
Gabriel N. Gatica, Martin Healey and Norbert Heuer
Numer. Methods Partial Differential Eq. 25 (6), 1303-1319, 2009.
On open surfaces, the energy space of hypersingular operators is a fractional
order Sobolev space of order 1/2 with homogeneous Dirichlet boundary condition
(along the boundary curve of the surface) in a weak sense. We introduce a
boundary element Galerkin method where this boundary condition is incorporated
via the use of a Lagrangian multiplier. We prove the quasi-optimal convergence
of this method (it is slightly inferior to the standard conforming method) and
underline the theory by a numerical experiment.
The approach presented in this paper is not meant to be a competitive
alternative to the conforming method but rather the basis for non-conforming
techniques like the mortar method, to be developed.