An Introduction to the Finite Element Method for Differential Equations. Mohammad Asadzadeh
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An Introduction to the Finite Element Method for Differential Equations
M. Asadzadeh
This edition first published 2021.
© 2021 John Wiley & Sons, Inc.
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The right of Mohammed Asadzadeh to be identified as the author of this work has been asserted in accordance with law.
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Library of Congress Cataloging‐in‐Publication Data
Names: Asadzadeh, M., author.
Title: An introduction to the finite element method for differential
equations / M. Asadzadeh.
Description: Hoboken, NJ : Wiley, [2020] | Includes bibliographical
references and index.
Identifiers: LCCN 2020008313 (print) | LCCN 2020008314 (ebook) | ISBN
9781119671640 (cloth) | ISBN 9781119671671 (adobe pdf) | ISBN
9781119671664 (epub)
Subjects: LCSH: Finite element method. | Differential equations.
Classification: LCC TA347.F5 A83 2020 (print) | LCC TA347.F5 (ebook) |
DDC 515/.35--dc23
LC record available at https://lccn.loc.gov/2020008313
LC ebook record available at https://lccn.loc.gov/2020008314
Cover Design: Wiley
Cover Image: Courtesy of: Mohammad Asadzadeh and Larisa Beilina
Preface
This book is an introduction to finite element methods (FEMs) used in the numerical solution of differential equations based on the piecewise polynomial approximations of the solutions. The presented material is accessible for upper undergraduates and starting graduate students in natural science and engineering. We mention three books for further and deeper study of FEM for differential equations.
Brenner, S.C. and Scott, L.R. The Mathematical Theory of Finite Element Methods. Springer, ed 3, 2017.
Ern, A. and Guermond, J.‐L. Theory and Practice of Finite Elements. Springer, 2004.
Larsson, S. and Thomée, V. Partial Differential Equations with Numerical Methods. Springer, 2003.
The material is presented in three main theme.
(I) Basic theory: Chapters 1 and 2, contains introduction (and in some extend derivation) of basic ordinary and partial differential equations,