STABILITY, CONVERGENCE AND ORDER OF THE EXTRAPOLATIONS OF THE RESIDUAL SMOOTHING SCHEME IN ENERGY NORM

Q4 Mathematics

Confluentes Mathematici Pub Date : 2011-11-20 DOI:10.1142/S1793744211000436

M. Ribot, M. Schatzman

引用次数: 3

Abstract

The Residual Smoothing Scheme is a numerical method which consists in preconditioning at each time step the method of lines. In this paper, RSS is defined and analyzed in an abstract linear parabolic case, i.e. for an abstract ordinary differential equation of the form with A a self-adjoint non negative operator, and it can be written where B is a preconditioner of A. We show that RSS is stable, convergent and of order one in energy norm. We also prove that its kth Richardson's extrapolation is stable and of order k.

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能量范数下残差平滑格式外推的稳定性、收敛性和阶数

残差平滑方案是一种数值方法，它包括在每个时间步对直线方法进行预处理。本文在抽象的线性抛物情形下定义并分析了RSS，即对于具有A为自伴随非负算子的抽象常微分方程，它可以表示为，其中B是A的前置条件。我们证明了RSS是稳定的，收敛的，在能量范数上是1阶的。我们还证明了它的第k个Richardson外推是稳定的，并且是k阶的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.