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

      © 2021 John Wiley & Sons, Inc.

      All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

      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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      While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

       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

      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,

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