Unique continuation for the Helmholtz equation using stabilized finite element methods (Q2274014)

The Helmholtz equation is considered and a computational approach based on a stabilized finite element method is introduced to treat the continuation process. Assuming convex geometry conditional stability estimates are derived with constants that grow at most linearly in the wave number. These estimates are used to obtain error bounds for the finite element method which are explicit with respect to the wave number. Numerical results are presented.