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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...
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...
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...
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.
In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
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...
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...
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 in -norm and in -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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