# (Communication) Unique continuation for the Helmholtz equation: stability estimates and stabilized FEM, by M. Nechita

We announce the communication within the Institute Seminar, for Wednesday, July 18, 2018, 11:00:

#### Unique continuation for the Helmholtz equation: stability estimates and stabilized FEM

by M. Nechita,

ICTP and Univ. College London (UCL) – PhD programme

Abstract. We will discuss the unique continuation problem for the Helmholtz equation and a numerical method for solving it based on stabilized finite elements. We will highlight the ill-posedness of the problem and, in the first part of the talk, focus on recently obtained conditional stability estimates. Taking an optimization approach, a stabilized finite element method will be introduced to solve the problem computationally. The FEM error bounds are explicit with respect to the wave number and are based on the continuum stability estimates. We will conclude with some numerical illustrations and a short example of a FEniCS-based implementation.
This talk is based on joint work with Erik Burman and Lauri Oksanen (https://arxiv.org/abs/1710.04125).