ABSTRACT
The interior Helmholtz problem with Dirichlet boundary condition is presented as:
Δ + = , , , ,
⎧⎨⎩ u u
u g= κ 2 0 in
on Ω Γ
(1.4)
in which, let us note that κ 2 cannot be a Dirichlet eigenvalue for −Δ on Ω, for frequencies f in (1.2) small enough and therefore the continuous problem has a unique solution. Without this assumption, the Helmholtz operator is singular and there is either no solution or as infinite set of solution to (1.4). Thus, this is important to do sufficiently accurate discrete approximations.
