A Posteriori analysis of a multirate numerical method for ordinary differential equations

被引：15

作者：

Estep, D. ^{[1
]}

Ginting, V. ^{[2
]}

Tavener, S. ^{[3
]}

机构：

[1] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA

[2] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

[3] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2012年 / 223卷

基金：

美国国家科学基金会; 美国国家卫生研究院; 美国国家航空航天局;

关键词：

Adjoint operator; A posteriori estimates; Discontinuous Galerkin method; Iterative method; Multirate method; Multiscale integration; Operator decomposition; ADAPTIVE GALERKIN METHODS; GLOBAL ERROR CONTROL; STABILITY PROPERTIES; CONSERVATION-LAWS; VARYING TIME; ONE-STEP; APPROXIMATIONS; CONVERGENCE;

D O I：

10.1016/j.cma.2012.02.021

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model. The main purpose of this paper is to present a hybrid a priori - a posteriori error analysis that accounts for the effects of projections between the coarse and fine scale discretizations, the use of only a finite number of iterations in the iterative solution of the discrete equations, the numerical error arising in the solution of each component, and the effects on stability arising from the multirate solution. The hybrid estimate has the form of a computable a posteriori leading order expression and a provably-higher order a priori expression. We support this estimate by an a priori convergence analysis. We present several examples illustrating the accuracy of multirate integration schemes and the accuracy of the a posteriori estimate. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：10 / 27

页数：18

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