中文摘要：

最近几年来,茅德康等发展了一类有限体积格式计算偏微分方程[1,3-4,6-9].该类格式得到比较好的计算结果.在文[8]中王和茅提出一个满足两个守恒律和三个守恒律的熵格式计算线性发展方程,但是该格式是基于线性多项式重构.本文发展了一个基于二次多项式重构满足两个守恒律的熵格式.数值试验表明本文的格式在长时间计算方面优于文[8].

英文摘要：

In recent years, MAO and his co-workers developed a class of finite-volume schemes for evolution partial differential equations[l＇3-4＇6-9]. Numerical experiments showed the efficiency of the method. In [8], WANG and MAO proposed an entropy scheme satisfying two conversation laws and three conversation laws, but the reconstruction based on linear polynomial for linear advection equa- tion. In this paper, we develop an entropy scheme with quadratic polynomial reconstruction satisfy- ing two conversation laws for linear advection equation. Numerical experiments show that our scheme is more robust in long-time behaviors than that of [8].