# Least-squares for linear elasticity eigenvalue problem

@article{Bertrand2020LeastsquaresFL, title={Least-squares for linear elasticity eigenvalue problem}, author={Fleurianne Bertrand and Daniele Boffi}, journal={ArXiv}, year={2020}, volume={abs/2003.00449} }

We 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.

#### 2 Citations

On the spectrum of the finite element approximation of a three field formulation for linear elasticity

- Computer Science, Mathematics
- ArXiv
- 2021

This paper considers a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity and discusses in particular the distribution of the discrete eigen values in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. Expand

DPG approximation of eigenvalue problems

- Mathematics, Computer Science
- ArXiv
- 2020

This paper considers in particular the primal and ultra weak formulations of the Laplace eigenvalue problem and proves the convergence together with a priori error estimates and proposes two possible error estimators. Expand

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