Least-squares formulations for eigenvalue problems associated with linear elasticity
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AbstractWe study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates and we confirm the theoretical results with simple two-dimensional numerical experiments.
CitationBertrand, F., & Boffi, D. (2021). Least-squares formulations for eigenvalue problems associated with linear elasticity. Computers & Mathematics with Applications. doi:10.1016/j.camwa.2020.12.013
SponsorsThe first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft, Germany in the Priority Program SPP 1748 Reliable simulation techniques in solid mechanics, Development of non standard discretization methods, mechanical and mathematical analysis under the project number BE 6511/1-1.The second author is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.
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