A Mixed Finite Element Methods For Solving Radiation Heat Equation Simplified Model

Inertial confinement fusion is an important way for achieving thermonuclear fusion. The research in this field is of great important since it will provide clean energy for the development of national economy.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.Firstly, aiming at the second-order elliptic scalar jump coefficient problem, using the RT mixed linear finite element, for two different types of interfaces and various types of boundary conditions, from the theoretical analysis and the numerical calculus two angles, we make a more systematic research work, obtain the super-convergence results of numerical solution under the jump coefficient situation, and construct the high accuracy calculation formula on the interfaces, and design a kind of fast algorithm based on the Scaling technical to the discrete saddle point system, and perform the massive numerical experiments to verify the correctness of the theoretical results on the basis of this. Secondly, we promote the text of the above results to two-dimensional three-radiation heat conduction equation simplified model of the numerical solution, because this problem is a typical multi-media estimation problem, therefore obtain the quite ideal computed result.