Overview
- Introduces the theoretical foundation of FE method and MFE method systematically
- Presents to readers with simple words which is easy to understand
- Provides latest research results of the reduced-dimension theory and methods
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About this book
This book aims to provide with some approaches for lessening the unknowns of the FE methods of unsteady PDEs. It provides a very detailed theoretical foundation of finite element (FE) and mixed finite element (MFE) methods in the first 2 chapters, and then Chapter 3 provides the FE and MFE methods to solve unsteady partial differential equations (PDEs). In the following 2 chapters, the principle and application of two proper orthogonal decomposition (POD) methods are introduced in detail.
This book can be used as both the introduction of FE method and the gateway to the FE frontier. For readers who want to learn the FE and MFE methods for solving various steady and unsteady PDEs, they will find the first 3 chapters very helpful. While those who care about engineering applications may jump to the last 2 chapters that introduce the construction of dimension reduction models and their applications to practical process calculations. This part could help them to improve the calculation efficiency and save CPU runtime so as to do wonders for their engineering calculations.
Keywords
Table of contents (5 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the author
Zhendong Luo has been engaged in the research on numerical solutions of partial differential equations (PDEs) in computational mathematics since 1986. His main research interests are finite element method and computational fluid dynamics and its numerical simulation. He has hosted and participated in more than 20 scientific research projects supported by National Natural Science Foundation of China or provincial and ministerial department. Luo has published a monograph and more than 260 research papers.
Bibliographic Information
Book Title: Finite Element and Reduced Dimension Methods for Partial Differential Equations
Authors: Zhendong Luo
DOI: https://doi.org/10.1007/978-981-97-3434-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Science Press 2024
Hardcover ISBN: 978-981-97-3433-7Published: 31 August 2024
Softcover ISBN: 978-981-97-3436-8Due: 14 September 2025
eBook ISBN: 978-981-97-3434-4Published: 30 August 2024
Edition Number: 1
Number of Pages: XXIII, 652
Number of Illustrations: 40 b/w illustrations, 68 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Analysis