mathematical theory of finite element methods 2e brenner [pdf]
The Mathematical Theory of Finite Element Methods (2E) by Susanne Brenner, L. Ridgway Scott
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About this book :-
The Mathematical Theory of Finite Element Methods written by
Susanne Brenner, L. Ridgway Scott .
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. This expanded second edition contains new chapters on additive Schwarz preconditioners and adaptive meshes. New exercises have also been added throughout. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests.
Book Detail :-
Title: The Mathematical Theory of Finite Element Methods
Edition: Second Edition
Author(s): Susanne Brenner, L. Ridgway Scott
Publisher: Springer New York
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About Author :-
The author Susanne Cecelia Brenner is an American mathematician. She was known because of her work in finite element method and related techniques for the numerical solution of differential equations.
Brenner did her undergraduate studies in mathematics and German at West Chester State College and received a master's degree in mathematics from SUNY Stony Brook. She obtained her Ph.D. from the University of Michigan in 1988 under the joint supervision of Jeffrey Rauch and L. Ridgway Scott; her thesis was entitled "Multigrid Methods for Nonconforming Finite Elements".
She holds a joint appointment with the Department of Mathematics and Center for Computation and Technology (CCT). At CCT she is also serving as the Associate Director for Academic Affairs since 2008. She is a Boyd Professor at Louisiana State University. In 2005 she was awarded a Humboldt-Forschungspreis (Humboldt Research Award) from the German Alexander von Humboldt Foundation. In 2011 she was awarded the AWM-SIAM Sonia Kovalevsky Lecture Prize. She is a SIAM Fellow (Class of 2010), AMS Fellow (Inaugural Class 2013), AAAS Fellow (2012), and AWM Fellow (2020). During 2021-2022 she is serving as President of the Society for Industrial and Applied Mathematics (SIAM). She currently chairs the editorial committee of the journal Mathematics of Computation.
The author L. Ridgway Scott is an American mathematian. He was known because of his work in spectral techniques for solving partial differential equations. He is professor emeritus at the University of Chicago. He was Professor of Computer Science and of Mathematics at the University of Chicago from 1998 to 2017, and the Louis Block Professor since 2001.
He obtained the B. S. degree (Magna Cum Laude) from Tulane University in 1969 and the Ph. D. degree in Mathematics from the Massachusetts Institute of Technology in 1973. He was an L. E. Dickson Instructor in Mathematics at the University of Chicago from 1973-1975. From 1975-1978 he held positions at the Brookhaven National Laboratory. In 1978, he was appointed Assistant Professor of Mathematics at the University of Michigan in Ann Arbor. In 1980, he was promoted to Associate Professor of Mathematics, with tenure, and in 1984 he was promoted to the rank of Professor. At Michigan, Professor Scott was a founding member of the Advanced Computer Architecture Laboratory, an early center for the study of parallel computing and a ``beta-site" for one of the first-generation of hypercube computers, the nCUBE-1.
In 1986, he became Professor of Computer Science and of Mathematics at the Pennsylvania State University where he helped to establish a program in parallel scientific computing which became a ``beta-site" for the second-generation Intel hypercube, the iPSC-2. He also co-founded what later became the W.G. Pritchard Fluid Mechanics Laboratory at Penn State.
At the University of Houston, Professor Scott continued his research on the finite element method as well as parallel computing. In addition, he initiated collaborations with researchers in the Department of Chemistry at the University of Houston and at Baylor College of Medicine to develop enhanced computational techniques in structural biology. From 1992 to 1998, he was the Director of the Texas Center for Advanced Molecular Computation, a National Science Foundation Grand Challenge Application Group. At the University of Chicago, Professor Scott is continuing his research in all of these areas. He was a Member of the Executive Committee of the ASCI Flash Center and is a founding member of the Institute for Biophysical Dynamics at the University of Chicago. He was a founding co-Director of the Argonne/Chicago Computation Institute which was established in spring, 1999.
He was also the director of the University of Chicago partnership in the The National Partership for Advanced Ccomputational Infrastructure (NPACI) based at SCSC/UCSD. Professor Scott has published over one hundred eighty papers, and five books, extending over biophysics, parallel computing and fundamental computational aspects of structural mechanics, fluid dynamics, nuclear engineering, and computational chemistry.
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Book Contents :-
The Mathematical Theory of Finite Element Methods written by
Susanne Brenner, L. Ridgway Scott
cover the following topics.
0. Basic concepts
1. Sobolev Spaces
2. Variational Formulation of Ellipse Boundary Value Problems
3. The construction of Finite Element Space
4. Polynomial Approximation Theory Elements
5. n-Dimensional Variational Problems
6. Finite Element Multigrid Methods
7. Additive Sehwarz Preconditioners
8. Max-norm Estimates
9. Adaptive Mesbes
10. Variational Crimes
11. Applicatios to Planar Elasticity
12. Mixed Methods
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