The Finite Element Method: An Introduction with Partial Differential Equations

Hardcover | October 22, 2011

byA. J. Davies

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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 isdeveloped 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 examplesthroughout and each chapter has a set of exercises with detailed solutions.

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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 isdeveloped for the solution of Poisson's equation...

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 ...

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Format:HardcoverDimensions:312 pages, 9.69 × 6.73 × 1.3 inPublished:October 22, 2011Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199609136

ISBN - 13:9780199609130

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Table of Contents

1. Historical introduction2. Weighted residual and variational methods3. The finite element method for elliptical problems4. Higher-order elements: the isoparametric concept5. Further topics in the finite element method6. Convergence of the finite element method7. The boundary element method8. Computational aspects9. ReferencesAppendicesA. Partial differential equation models in the physical sciencesB. Some integral theorems of the vector calculusC. A formula for integrating products of area coordinates over a triangleD. Numerical integration formulaeE. Stehfest's formula and weights for numerical Laplace transform inversion