Solín Partial Differential Equations and the Finite Element Method

1. Auflage 2005
ISBN: 978-0-471-76409-0
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 512 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

A systematic introduction to partial differential
equations and modern finite element methods for their efficientnumerical solution
Partial Differential Equations and the Finite Element Methodprovides a much-needed, clear, and systematic introduction tomodern theory of partial differential equations (PDEs) and finiteelement methods (FEM). Both nodal and hierachic concepts of the FEMare examined. Reflecting the growing complexity and multiscalenature of current engineering and scientific problems, the authoremphasizes higher-order finite element methods such as the spectralor hp-FEM.
A solid introduction to the theory of PDEs and FEM contained inChapters 1-4 serves as the core and foundation of the publication.Chapter 5 is devoted to modern higher-order methods for thenumerical solution of ordinary differential equations (ODEs) thatarise in the semidiscretization of time-dependent PDEs by theMethod of Lines (MOL). Chapter 6 discusses fourth-order PDEs rootedin the bending of elastic beams and plates and approximates theirsolution by means of higher-order Hermite and Argyris elements.Finally, Chapter 7 introduces the reader to various PDEs governingcomputational electromagnetics and describes their finite elementapproximation, including modern higher-order edge elements forMaxwell's equations.
The understanding of many theoretical and practical aspects of bothPDEs and FEM requires a solid knowledge of linear algebra andelementary functional analysis, such as functions and linearoperators in the Lebesgue, Hilbert, and Sobolev spaces. Thesetopics are discussed with the help of many illustrative examples inAppendix A, which is provided as a service for those readers whoneed to gain the necessary background or require a refreshertutorial. Appendix B presents several finite element computationsrooted in practical engineering problems and demonstrates thebenefits of using higher-order FEM.
Numerous finite element algorithms are written out in detailalongside implementation discussions. Exercises, including manythat involve programming the FEM, are designed to assist the readerin solving typical problems in engineering and science.
Specifically designed as a coursebook, this student-testedpublication is geared to upper-level undergraduates and graduatestudents in all disciplines of computational engineeringandscience. It is also a practical problem-solving reference forresearchers, engineers, and physicists.

Autoren/Hrsg.

Solín, Pavel

Inhaltsverzeichnis

List of Figures.
List of Tables.
Preface.
Acknowldegments.
1. Partial Differential Equations.
2. Continuous Elements for 1D Problems.
3. General Concept of Nodal Elements.
4. Continuous Finite Elements for 2D Problems.
5. Transient Problems and ODE Solvers.
6. Beam and Plate Bending Problems.
7. Equations of Electrimagnetics.
Appendix A: Basics of Functional Analysis.
Appendix B: Software and Examples.
References.
Index.

Über Autor(innen)

PAVEL SOLÍN, PhD, is Associate Professor in the Department of Mathematical Sciences at The University of Texas at El Paso. Prior to this appointment, Dr. Solin was a postdoctoral research associate at the Johannes Kepler University (Linz, Austria), The University of Texas at Austin, and Rice University (Houston, Texas). He received his PhD from the Charles University in Prague, Czech Republic, in 1999. Dr. Sol?n is a coauthor of the monograph Higher-Order Finite Element Methods.