一个刚性守恒律方程组的全隐式差分方法  

THE FULLY IMPLICIT DIFFERENCE METHODS FOR A STIFF SYSTEM OF CONSERVATION LAWS

作　　者：汤华中[1,2] 

机构地区：[1]中科院数学与系统科学研究院计算数学所,科学与工程计算国家重点实验室 [2]北京大学数学科学院,北京100871

出　　处：《计算数学》2001年第2期129-138,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(19901031);计算物理实验室基金

摘　　要：This paper is interested in a system of conservation laws with a stiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite difference methods approximating this system are analyzed, which include maximum principles, bounds on the total variation, Ll-bounds, and L1-continuity estimates in term of some conserved physical quantity and this characteristic variables generated by difference schemes with proper initial data. These estimates are necessary for the existence of a bounded-total variation (BV) solution. Furthermore, we show that numerical entropy inequalities for some convex entropy pairs of the fully system hold.This paper is interested in a system of conservation laws with a stiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite difference methods approximating this system are analyzed, which include maximum principles, bounds on the total variation, Ll-bounds, and L1-continuity estimates in term of some conserved physical quantity and this characteristic variables generated by difference schemes with proper initial data. These estimates are necessary for the existence of a bounded-total variation (BV) solution. Furthermore, we show that numerical entropy inequalities for some convex entropy pairs of the fully system hold.

关 键 词：有限差分格式 双曲型守恒律 数值熵条件 特征值 全隐式差分格式 刚性守恒律方程组 

分 类 号：O241[理学—计算数学]