Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms
Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms
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DOI：
10.1007/978-3-642-61623-5
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发表时间：
1986-06
期刊：
影响因子：
--
通讯作者：
V. Girault;P. Raviart
中科院分区：
文献类型：
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作者：
V. Girault;P. Raviart
材料所涵盖的这本书已教的作者之一，在研究生课程的数值分析在大学皮埃尔等玛丽居里的巴黎。这是一个扩展版本的前一个文本（cf. Girault & Raviart [32 J]）出版于1979年的Springer-Verlag系列：Lecture Notes in Mathematics。在过去的十年中，许多工程师和数学家都集中精力在不可压缩流动的Navier-Stokes方程的有限元解上。这本书的目的是对该领域的最新发展提供一个相当详尽的论述。为了保持在合理的范围内，我们已经限制自己的情况下，平稳的问题，虽然时间相关的问题是根本的重要性。这一主题目前正在迅速发展，我们认为它值得被另一个专门的专著所涵盖。我们已尽了最大的努力，对内流的有限元法作了相当详尽的处理。然而，在另一方面，我们完全忽略了外部问题的主题，这些问题涉及从理论和实践的观点来看完全不同的技术。此外，我们既没有讨论本书所提出的有限元方法的实现，也没有给出任何显式的数值结果。Peyret & Taylor [64]和Peyasset [82]广泛涵盖了这一领域。
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].