A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity∗
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
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∗
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 Higher Order Mixed Finite Element Methods for Plane Elasticity.
A Family of Mixed Finite Elements for Linear Elasticity.
A Family of Mixed Finite Elements for the Elasticity Problem.
A finite dimensional linear programming approximation of Mather's variational problem
We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
A finite element analysis for elastoplastic bodies obeying Hencky's law
Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.
A finite element analysis for the Signorini problem in plane elastostatics
A finite element discretization of the contact between two membranes
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.
A finite element discretization of the contact between two membranes
From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.
A Finite Element Lumped Mass Scheme for Solving Eigenvalue Problems of Circular Arches.
A Finite Element Lumped Mass Scheme for Solving Eigenvalue Problems of Circular Arches.
A finite element method for stiffened plates
The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...
A finite element method for stiffened plates
The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...
A finite element scheme for the evolution of orientational order in fluid membranes
We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, J. Phys. II7 (1997) 1509–1520; N. Uchida, Phys. Rev. E66 (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce...
A finite element solution for plasticity with strain-hardening
A Finite-Difference Approximation for the Eigenvalue of the Clamped Plate.
A fixed point method in dynamic processes for a class of elastic-viscoplastic materials
Two problems are considered describing dynamic processes for a class of rate-type elastic-viscoplastic materials with or without internal state variable. The existence and uniqueness of the solution is proved using classical results of linear elasticity theory together with a fixed point method.