二维辐射热传导方程的渐近展开方法

Asymptotic Expansion Methods for 2-D Radiation Heat Conduction Equations

二维辐射热传导方程是具有多尺度、强间断等性质的方程,渐近展开方法是求解这类方程的一种有效的方法,其基本思想是将具有多尺度性质的椭圆型向量问题解耦为若干光滑系数(或单尺度性质)的椭圆型向量问题进行求解.针对二维辐射热传导方程的简化线性模型,设计并分析了基于渐近展开方法的线性有限元方法,并给出了相应的误差估计式.

2-D radiation heat conduction equations have multi-scale characteristic and strong discontinuity. The asymptotic expansion method is effective to solve such problems,whose main idea is to decompose the elliptic vector equation with multi-scale characteristic into several elliptic vector equation with smooth (or single-scale characteristic) coefficients.For a kind of linear radiation heat conduction equations,this paper designs and analyzes a linear finite element method based on the asymptotic expansion,and gives corresponding error estimation.