Unique continuation for the Helmholtz equation using stabilized finite element methods
Provides theoretical error estimates for an ill-posed inverse problem in wave propagation, relevant for computational acoustics and electromagnetics.
The authors develop a stabilized finite element method for the Helmholtz equation unique continuation problem, deriving wave-number-explicit error bounds with constants growing at most linearly in the wave number under convex geometry assumptions.
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity assumption on the geometry, the constants grow at most linearly in the wave number. Then these estimates are used to obtain error bounds for the finite element method that are explicit with respect to the wave number. Some numerical illustrations are given.