Unique continuation for the Lamé system using stabilized finite element methods

Autor: Erik Burman, Janosch Preuss
Rok vydání: 2023
Předmět:
Zdroj: GEM - International Journal on Geomathematics. 14
ISSN: 1869-2680
1869-2672
DOI: 10.1007/s13137-023-00220-1
Popis: We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove convergence rates for the proposed method which take into account the noise level and the polynomial degree. A series of numerical experiments corroborates our theoretical results and explores additional aspects, e.g. how the quality of the reconstruction depends on the geometry of the involved domains. We find that certain convexity properties are crucial to obtain a good recovery of the wave displacement outside the data domain and that higher polynomial orders can be more efficient but also more sensitive to the ill-conditioned nature of the problem.
36 pages, 10 figures
Databáze: OpenAIRE
Externí odkaz: