Oanh Chau

Analysis of a class of dynamic thermal contact problems

We study a general system defined by a second order evolution equation, coupled with a first order differential equation, which can model some classes of dynamic thermal contact problems. We present and establish an existence and uniqueness result, by using general results on evolution equations and Banachs contraction principle, with monotone operators and fixed point arguments. Then a fully discrete scheme for numerical approximations and analysis of error order estimate are provided. Finally applications to concrete dynamic contact problems are given, followed by numerical simulations.

An Adaptive Finite Element Method for Solving a Free Boundary Problem with Periodic Boundary Conditions in Lubrication Theory

A duality approximation method combined with an adaptive finite element method is applied to solve a free boundary problem with periodic boundary conditions in lubrication theory.

Numerical Analysis for a Class of Non Clamped Contact Problems

We study a class of dynamic thermal sub-differential contact problems with friction, for long memory viscoelastic materials, without the clamped condition, which can be put into a general model of system defined by a second order evolution inequality, coupled with a first order evolution equation. After statement of an existence and uniqueness result, we present a fully discrete scheme for numerical approximations and analysis of error order estimate.

Numerical treatment of a class of thermal contact problems

A mathematical problem modeling dynamical behavior of viscoelastic materials is studied. The problem is related to highly nonlinear and non-smooth phenomena like contact, friction and a class of dynamic contact problems with friction and thermal effects. The applied approach leads to a system involving variational inequalities and a fully discrete scheme for numerical approximations and the analysis of error estimate order is provided. Numerical computations are given so as to illustrate the mathematical model.

On some dynamic thermal non clamped contact problems

We study a class of dynamic thermal sub-differential contact problems with friction, for long memory visco-elastic materials, without the clamped condition, which can be put into a general model of system defined by a second order evolution inequality, coupled with a first order evolution equation. We present and establish an existence and uniqueness result, by using general results on first order evolution inequality, with monotone operators and fixed point methods. Finally a fully discrete scheme for numerical approximations is provided, and corresponding various numerical computations in dimension two will be given.

A Non-clamped Frictional Contact Problem with Normal Compliance

In this chapter we study a dynamic frictional contact problem with normal compliance and non-clamped contact conditions, for thermo-viscoelastic materials. The weak formulation of the problem leads to a general system defined by a second order quasivariational evolution inequality coupled with a first order evolution equation. We state and prove an existence and uniqueness result, by using arguments on parabolic variational inequalities, monotone operators and fixed point. Then, we provide a numerical scheme of approximations and various numerical computations.