Two-grid Methods For The Model Of 2-D Heat Conduction With Three-temperature

Two dimensional heat conduction equation with three temperature is an important model in the simulation of inertial confinement fusion (ICF), which approximately describes the process of radiant energy broadcasting in the quiescent medium and energy exchange of electrons with photons and irons. In this paper, using the finite element method, we discuss the two-grid methods for two simplified models.In the first part, for a linear equation of 2-D heat conduction with three-temperature, we propose two kinde of two-grid method, which are called as Algorithm 2.1 and 2.2. Using the theory of the finite element method (FEM), we give the error estimates of these algorithms are O(h) , which are the same as that of commonly used FEM. The numerical experiments verify the correctness of theoretical results.In the second part, for a nonlinear equation of 2-D heat conduction with three-temperature, we give two kinds of two-grid method, which are called as Algorithm 3.2 and 3.3. Some theoretical analysis are provided for the error estimates of the two algorithms. The resulting new methods are shown, by numerical experiments, to be much more efficient and robust than commonly used FEM.