The Finite Element Method Of Non-Fourier Heat Conduction Problem Under The Mixed Boundary Condition

In this paper,the finite element method for evolution equation is used to solve the Non-Fourier heat conduction problem with Dirichlet-Neumann mixed boundary condi-tion.This kind of problem introduce the hyperbolic-parabolic type partial differential equation to describe the Non-Fourier effect in solid materials under laser irradiation.We give the semi-discrete scheme in space direction by Galerkin method for the Non-Fourier heat conduction problem,stability and convergence of the semi-discrete scheme are proved.Furthermore,the Du Fort-Frankel difference scheme is used in the time direction to obtain the fully discrete shcheme,then the convergence of the fully dis-crete scheme is proved.In this paper,numerical experiments for different type of model problems are performed.Numerical results show that the Du Fort-Frankel fully discrete scheme given for the mixed boundary condition of Non-Fourier problem is effective and efficient,and its convergence is consistent with the theoretical analysis results.