Unique continuation for the Helmholtz equation using stabilized finite element methods
Numerical Analysis
2018-10-29 v2 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.1710.04125,
title = {Unique continuation for the Helmholtz equation using stabilized finite element methods},
author = {Erik Burman and Mihai Nechita and Lauri Oksanen},
journal= {arXiv preprint arXiv:1710.04125},
year = {2018}
}
Comments
corrected typos; included suggestions from reviewers