Finite Element Methods for Nonlinear Shell Analysis.
Finite elements methods for solving viscoelastic thin plates
The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by -elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.
Finite volume schemes for the generalized subjective surface equation in image segmentation
In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set finite volume space discretization. The space discretization is discussed in details and we introduce three...
Finite volume schemes for the p-laplacian on cartesian meshes
This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite volume schemes for the p-Laplacian on Cartesian meshes
This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite-difference approximation of energies in fracture mechanics
Folded shells : a variational approach
Formulation mixte d'un problème de jonctions de poutres adaptée à la résolution d'un problème d'optimisation
Free energy and internal variables in linear viscoelasticity
In connection with the determination of the free energy functional for the viscoelastic stress tensor, a viscoelastic material is considered as described by a material with internal variables. In this framework the free energy is uniquely determined. It proves to be the minimal one in the class of thermodynamically admissible free energies.
Free vibration of layered circular cylindrical shells of variable thickness using spline function approximation.
Functional a posteriori error estimates for incremental models in elasto-plasticity
We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants...
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an...
Global Regular Solutions for the Dynamic Antiplane Shear Problem in Nonlinear Viscoelasticity.
Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation
Godunov method for nonconservative hyperbolic systems
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal Maso et al. [J. Math. Pures Appl.74 (1995) 483–548] is used in order to define the weak solutions of the system: an interpretation of the nonconservative products as Borel measures is given, based on the choice of a family of paths drawn in the phase space. Even if the family of paths can be chosen arbitrarily, it is natural to require this...
Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals
The paper is concerned with guaranteed and computable bounds of the limit (or safety) load, which is one of the most important quantitative characteristics of mathematical models associated with linear growth functionals. We suggest a new method for getting such bounds and illustrate its performance. First, the main ideas are demonstrated with the paradigm of a simple variational problem with a linear growth functional defined on a set of scalar valued functions. Then, the method is extended to...
-FEM for three-dimensional elastic plates
In this work, we analyze hierarchic -finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the -FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness tends to zero, the -discretization is consistent with the three-dimensional solution to any power of in the energy...
Hilbert transform and its geophysical applications
Homogénéisation