Finite Element Method

An Introduction with Partial Differential Equations
2. Auflage 2011
ISBN: 978-0-19-960913-0
Verlag: Oxford University Press(UK)

Buch, Englisch, 308 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 535 g

The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational
approach is also explained.

This book is written at an introductory level, developing all the necessary concepts where required. Consequently, it is well-placed to be used as a textbook for a course in finite elements for final year undergraduates, the usual place for studying finite elements. There are worked examples throughout and each chapter has a set of exercises with detailed solutions.

Zielgruppe

Suitable for undergraduate mathematicians, engineers, and physical scientists. It will also provide postgraduates and researchers in industry or academia a basis from which to move on to more advanced texts.

Autoren/Hrsg.

Davies, A J

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

1: Historical introduction
2: Weighted residual and variational methods
3: The finite element method for elliptical problems
4: Higher-order elements: the isoparametric concept
5: Further topics in the finite element method
6: Convergence of the finite element method
7: The boundary element method
8: Computational aspects
9: References
Appendices
A: Partial differential equation models in the physical sciences
B: Some integral theorems of the vector calculus
C: A formula for integrating products of area coordinates over a triangle
D: Numerical integration formulae
E: Stehfest's formula and weights for numerical Laplace transform inversion

Über Autor(innen)

Alan Davies is Professor of Mathematics at the University of Hertfordshire where his teaching and research is in numerical applied mathematics. He was the Head of the School of Physics, Astronomy and Mathematics until he retired in 2006 since when he has been able to concentrate on the communication of mathematics and physics through the department's outreach programme.