scholarly journals Variational and Numerical Analysis of a Static Thermo-Electro-Elastic Problem with Friction

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Othman Baiz ◽  
Hicham Benaissa ◽  
Driss El Moutawakil ◽  
Rachid Fakhar
Keyword(s):  
Frictional Contact ◽  
A Priori ◽  
Finite Element Approximation ◽  
Elastic Problem ◽  
Constitutive Law ◽  
Element Approximation ◽  
Coulomb’S Friction ◽  
Elliptic Variational Inequalities ◽  
Thermally Conductive ◽  
Priori Error Estimates

We consider a mathematical model which describes a static frictional contact between a piezoelectric body and a thermally conductive obstacle. The constitutive law is supposed to be thermo-electro-elastic and the contact is modeled with normal compliance and a version of Coulomb’s friction law. We derive a variational formulation of the problem and we prove the existence and uniqueness of its solution. The proof is based on some results of elliptic variational inequalities and fixed point arguments. Furthermore, a finite element approximation and a priori error estimates are obtained.

scholarly journals AN H1 -GALERKIN MIXED FINITE ELEMENT APPROXIMATION OF A NONLOCAL HYPERBOLIC EQUATION

2017 ◽  
Vol 22 (5) ◽  
pp. 643-653
Author(s):  
Fengxin Chen ◽  
Zhaojie Zhou
Keyword(s):  
Finite Element ◽  
Hyperbolic Equation ◽  
Mixed Finite Element ◽  
A Priori ◽  
Finite Element Approximation ◽  
Nonlinear Hyperbolic Equation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Priori Error Estimates

In this paper we investigate a semi-discrete H1 -Galerkin mixed finite element approximation of one kind of nolocal second order nonlinear hyperbolic equation, which is often used to describe vibration of an elastic string. A priori error estimates for the semi-discrete scheme are derived. A fully discrete scheme is constructed and one numerical example is given to verify the theoretical findings.

scholarly journals Crank-Nicolson Fully DiscreteH1-Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Fengxin Chen
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Time Derivative ◽  
Finite Element Approximation ◽  
Optimal Order ◽  
Element Approximation ◽  
Fully Discrete ◽  
Priori Error Estimates ◽  
Crank Nicolson

We consider a fully discreteH1-Galerkin mixed finite element approximation of one nonlinear integrodifferential model which often arises in mathematical modeling of the process of a magnetic field penetrating into a substance. We adopt the Crank-Nicolson discretization for time derivative. Optimal order a priori error estimates for the unknown function inL2andH1norm and its gradient function inL2norm are presented. A numerical example is given to verify the theoretical results.

A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

2014 ◽  
Vol 6 (5) ◽  
pp. 552-569 ◽  
Author(s):  
Wanfang Shen ◽  
Liang Ge ◽  
Danping Yang ◽  
Wenbin Liu
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
A Priori ◽  
Mathematical Formulation ◽  
Finite Element Approximation ◽  
A Priori Error Estimates ◽  
Element Approximation ◽  
Weak Formulation ◽  
Priori Error Estimates

AbstractIn this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in H1 and L2 norms. Furthermore some numerical tests are presented to verify the theoretical results.

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