The Numerical Analysis Of Non-Fourier Heat Conduction Problem

Firstly,we introduce the analytic solution of non-Fourier heat conduction problem in one-dimensional semi-infinite region by Laplace transform method,and we observe the characteristics of the analytic solutions by drawing their graphic.Secondly,we apply the finite element method of evolution equations to solve the non-Fourier heat conduction problem.The Galerkin semi-discrete scheme is given and its stability and convergence are proved.Then we use Du Fort-Frankel difference scheme in time direction to deduce the full discrete scheme,and we give the error estimates of the full discrete scheme.We calculate the non-Fourier problem in one-dimensional bounded domain,and the result show that the fully discrete scheme is effective and efficient.Finally,several difference schemes for non-Fourier heat conduction problem and their numerical results are given,also we analyzed the stability of Du Fort-Frankel difference scheme.