Open access peer-reviewed Edited Volume

Finite Element Methods and Their Applications

Mahboub Baccouch

University of Nebraska at Omaha


Two-Point Boundary-Value Problems Variational Formulation Finite Element Approximation Error Estimation Adaptive Methods Elliptic Problems Parabolic Problems Hyperbolic Problems Higher Order Equations A Priori Error Estimation A Posteriori Error Estimation Adaptive Mesh Refinement

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About the book

This book will cover the numerical and theoretical foundation of the finite element method as a general numerical method for solving ordinary and partial differential equations. It will address the Galerkin method for one-, two- and three-dimensional differential equations (including parabolic, hyperbolic and elliptic partial differential equations) and also convergence and stability criterion. Several continuous and discontinuous finite element methods and adaptive refinement strategies will also be introduced as well as the error estimation techniques for typical finite element methods.

Throughout the text the implementation and analysis of the involved algorithms will be emphasized. In addition, some theoretical aspects as existence, uniqueness, stability and convergence will be discussed together with some of the most important applications of finite elements and its basic methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

One objective of this book is to show the reader the basic tools for analyzing finite element methods while proofs of stability and convergence of the method will be given in more detail. Another objective is to familiarize the reader with the coding issues of finite element methods: data structure, construction of local matrices, and assembling of the global matrix. Several computational examples will also be provided. Finally, by presenting specific applications of finite element methods to important engineering problems, we hope to convince the reader that the finite element method is a competitive approach for solving many scientific problems.

Publishing process

Book initiated and editor appointed

Date completed: June 8th 2020

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: August 28th 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: November 16th 2020

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: January 15th 2021

All chapters are copy-checked and typesetted before being published. IntechOpen regularly submits its books to major databases for evaluation and coverage, including the Clarivate Analytics Book Citation Index in the Web of ScienceTM Core Collection. Other discipline-specific databases are also targeted, such as Web of Science's BIOSIS Previews.

About the editor

Mahboub Baccouch

University of Nebraska at Omaha

Mahboub Baccouch is currently a full professor of applied and computational Mathematics at the University of Nebraska at Omaha (UNO), USA. He received both B.S. (2004) and M.S. (2005) degrees in Engineering and Engineering Mathematics. In 2005, he received his second M.S. in Mathematics degree from Virginia Tech. He received his Ph.D. degree in Mathematics in May 2008 from Virginia Tech. He has been a tenure-track assistant professor in the department of Mathematics at UNO since Fall 2008. He was promoted to Associate Professor with tenure in the Fall of 2014. In Spring 2017, he received the James Earl Diamond Professorship in Mathematics, which is awarded for distinguished faculty performance in teaching and research. In Fall 2017, he received the College of Arts and Sciences Excellence in Research Award. In 2019, he was promoted to full professor. His research area of interest lies in computational and applied mathematics. He is currently investigating topics related to numerical methods for solving PDEs using high order methods including finite element and discontinuous Galerkin methods. He is also studying numerical solutions of mathematical problems using high order methods with broader applications. Recently, he began investigating a new research area related to numerical methods for stochastic differential equations.

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