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

共 27 条

[1] ERROR BOUNDS FOR NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS [J].

COOPER, GJ .

NUMERISCHE MATHEMATIK, 1971, 18 (02) :162-&

[2]

DAHLQUIST G, 1993, LECTURE NOTES

[3]

DAHLQUIST G, 1982, NUMERICAL INTEGRATIO, P97

[4]

Dekker K., 1984, STABILITY RUNGE KUTT

[5]

DELFOUR M, 1981, MATH COMPUT, V36, P455, DOI 10.1090/S0025-5718-1981-0606506-0

[6] SOME STABILITY ASPECTS OF SCHEMES FOR THE ADAPTIVE INTEGRATION OF STIFF INITIAL-VALUE PROBLEMS [J].

DIECI, L ;

ESTEP, D .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1991, 12 (06) :1284-1303

[7] ERROR-ESTIMATES AND AUTOMATIC TIME STEP CONTROL FOR NONLINEAR PARABOLIC PROBLEMS .1. [J].

ERIKSSON, K ;

JOHNSON, C .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (01) :12-23

[8] TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE DISCONTINUOUS GALERKIN METHOD [J].

ERIKSSON, K ;

JOHNSON, C ;

THOMEE, V .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1985, 19 (04) :611-643

[9] ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .1. A LINEAR-MODEL PROBLEM [J].

ERIKSSON, K ;

JOHNSON, C .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (01) :43-77

[10]

ERIKSSON K, ADAPTIVE FINITE EL 5

← 1 2 3 →