相关论文: On the spectrum of an operator associated with lea…

We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares…

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…

We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…

We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…

Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This…

In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lam\'e operators with non self-adjoint perturbations, we provide…

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…

In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…

For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.

We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…

A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analysed. In particular, the least-squares…

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle…

Here, we present a least-squares based spectral element formulation for one-dimensional eigenvalue problems with interface conditions. First we develop the method for without interface case, then we extend it to interface case. Convergence…

We discuss the determination of the Lam\'e parameters of an elastic material by the means of boundary measurements. We will combine previous results of Eskin-Ralston and Isakov to prove inverse results in the case of bounded domains with…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…

We obtain linear elasticity as $\Gamma$-limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.