A-POSTERIORI ERROR-BOUNDS AND GLOBAL ERROR CONTROL FOR APPROXIMATION OF ORDINARY DIFFERENTIAL-EQUATIONS

被引：141

作者：

ESTEP, D ^{[1
]}

机构：

[1] GEORGIA INST TECHNOL, SCH MATH, ATLANTA, GA 30332 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1995年 / 32卷 / 01期

关键词：

POSTERIORI ERROR BOUNDS; A PRIORI ERROR BOUNDS; ADAPTIVE ERROR CONTROL; CONTRACTIVE PROBLEMS; DISSIPATIVE PROBLEMS; DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD; GLOBAL ERROR CONTROL; ONE-STEP METHOD; ORDINARY DIFFERENTIAL EQUATION; STIFF PROBLEMS;

D O I：

10.1137/0732001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The author analyzes a finite element method for the integration of initial value problems in ordinary differential equations. General and contractive problems are treated, and quasioptimal a priori and a posteriori error bounds obtained in each case. In particular, good results are obtained for a class of stiff dissipative problems. These results are used to construct a rigorous and robust theory of global error control. The author also derives an asymptotic error estimate that is used in a discussion of the behavior of the error. In conclusion, the properties of the error control are exhibited in a series of numerical experiments.

引用

页码：1 / 48

页数：48

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