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A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity∗

Yongxing Shen, Adrian J. Lew (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k ≥ 1 for the approximation of the displacement field, and of order k or k − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

Yongxing Shen, Adrian J. Lew (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k ≥ 1 for the approximation of the displacement field, and of order k or k − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in both cases, with error estimates that are independent...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity∗

Yongxing Shen, Adrian J. Lew (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order k ≥ 1 for the approximation of the displacement field, and of order k or k − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields...

A note on prestressed thermoelastic bodies.

Ramón Quintanilla (1991)

Collectanea Mathematica

This note is concerned with the ill-posed problem for prestressed thermoelastic bodies. Under suitable hypotheses for the thermoelastic coefficients, the domain and the behavior of solutions at infinity, we prove uniqueness of the solutions. We also obtain some estimates for the solutions related with the initial condition.

An energy-preserving Discrete Element Method for elastodynamics∗

Laurent Monasse, Christian Mariotti (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...

An energy-preserving Discrete Element Method for elastodynamics∗

Laurent Monasse, Christian Mariotti (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...

An equilibrium finite element method in three-dimensional elasticity

Michal Křížek (1982)

Aplikace matematiky

The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates O ( h 2 ) in L 2 -norm and O ( h 1 / 2 ) in L ∞ -norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.

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