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In this paper we analyze a mixed displacement‐pseudostress formulation for the 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 not introduce spurious modes. Error estimates for the proposed method are derived. Finally, we report some numerical tests supporting the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected. [ABSTRACT FROM AUTHOR]