5 research outputs found
Computation of eigenvalues in linear elasticity with least-squares finite elements:dealing with the mixed system
In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.</p
On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity
In this paper we provide some more details on the numerical analysis and we
present some enlightening numerical results related to the spectrum of a finite
element least-squares approximation of the linear elasticity formulation
introduced recently. We show that, although the formulation is robust in the
incompressible limit for the source problem, its spectrum is strongly dependent
on the Lam\'e parameters and on the underlying mesh.Comment: 21 pages, 14 figure
Computation of Eigenvalues in Linear Elasticity with Least-Squares Finite Elements: Dealing with the Mixed System
In this paper we discuss some aspects related to the practical implementation
of a method that has been introduced recently for the approximation of the eigenvalues of the
linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives
rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the
algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the
convergence of the scheme should be carefully interpreted
Computation of eigenvalues in linear elasticity with least-squares finite elements: dealing with the mixed system
In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted