A non-conforming domain decomposition approximation for the
Helmholtz screen problem with hypersingular operator
Norbert Heuer and Gredy Salmerón
Numer. Methods Partial Differential Eq. 33 (1), 125-141, 2017.
We present and analyze a non-conforming domain decomposition approximation
for a hypersingular operator governed by the Helmholtz equation in three dimensions.
This operator appears when considering the corresponding Neumann problem in
unbounded domains exterior to open surfaces. We consider small wave numbers
and low-order approximations with Nitsche coupling across interfaces.
Under appropriate assumptions on mapping properties of the weakly singular
and hypersingular operators with Helmholtz kernel, we prove that this method
converges almost quasi-optimally. Numerical experiments confirm our error estimate.