相关论文: Towards a unified analysis of mixed methods for el…

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 analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…

This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector…

In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…

A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…

We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…

We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a…

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…

The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…

We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…

In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a…

For a family of stabilized mixed finite element methods for the Stokes equations a complete a priori and a posteriori error analysis is given.

A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…