A Finite Element Approximation of a Variational Inequality Formulation of Bean's Model for Superconductivity

A Quasi-variational Inequality Problem in Superconductivity

We derive a class of analytical solutions and a dual formulation of a scalar two-space-dimensional quasi-variational inequality problem in applied superconductivity. We approximate this formulation by a fully practical ̄nite element method based on the lowest order Raviart Thomas element, which yields approximations to both the primal and dual variables (the magnetic and electric ̄elds). We prove...

Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity

PENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH COULOMB’S FRICTION FOR LOCKING MATERIAL

In this work, we study a unilateral contact problem with non local friction of Coulombbetween a locking material and a rigid foundation. In the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. In the second step, usingthe penalty method we...

Finite Element Analysis and Algorithms for Single-Crystal Strain-Gradient Plasticity

We provide optimal a priori estimates for nite element approximations of a model of rate-independent single-crystal strain-gradient plasticity. The weak formulation of the problem takes the form of a variational inequality in which the primary unknowns are the displacement and slips on the prescribed slip systems, as well as the back-stress associated with the vectorial microstress. It is shown...

On Fixed Point Results for Hemicontractive-type Multi-valued Mapping, Finite Families of Split Equilibrium and Variational Inequality Problems

In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algori...