A SECOND ORDER UNCONDITIONALLY CONVERGENT FINITE ELEMENT METHOD FOR THE THERMAL EQUATION WITH JOULE HEATING PROBLEM  

作　　者：Xiaonian Long Qianqian Ding 

机构地区：[1]College of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450045,China [2]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Journal of Computational Mathematics》2022年第3期354-372,共19页计算数学（英文）

摘　　要：In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

关 键 词：Thermal equation Joule heating Finite element method Unconditional convergence Second order backward difference formula Optimal L^(2)-estimate 

分 类 号：O24[理学—计算数学]