Daniel Inzunza, Felipe Lepe, Gonzalo Rivera:
Displacement-pseudostress formulation for the linear elasticity spectral problem: a priori analysis
In this paper we analyze a mixed displacement-pseudostress formulation for elasticity eigenvalue problem. We propose a finite element method to approximate the pseudostress tensor with Raviart-Thomas elements and the displacement with piecewise polynomials. With the aid of the classic theory for compact operators, we prove that our method is convergent and does no introduce spurious modes. Also, we obtain error estimates for the proposed method. Finally, we report some numerical test supporting the theoretical results.
This preprint gave rise to the following definitive publication(s):
Daniel INZUNZA, Felipe LEPE, Gonzalo RIVERA: Displacement-pseudostress formulation for the linear elasticity spectral problem. Numerical Methods for Partial Differential Equations, vol. 39, pp. 1996-2017, (2023).