The Finite Element Method For Elliptic Problems

Author : P.G. Ciarlet
Publisher : Elsevier
Page : 529 pages
File Size : 43,7 Mb
Release : 1978-01-01
Category : Mathematics
ISBN : 0080875254

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The Finite Element Method for Elliptic Problems by P.G. Ciarlet Pdf

The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments should provide many suggestions for conducting seminars.

Author : Philippe G. Ciarlet
Publisher : North-Holland
Page : 530 pages
File Size : 54,8 Mb
Release : 1978-01-01
Category : Boundary value problems
ISBN : 0444850287

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The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet Pdf

Author : P Ciarlet
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 2012
Category : Electronic
ISBN : 0444557172

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The Finite Element Method for Elliptic Problems by P Ciarlet Pdf

Author : Philippe G. Ciarlet
Publisher : SIAM
Page : 552 pages
File Size : 41,7 Mb
Release : 2002-04-01
Category : Mathematics
ISBN : 9780898715149

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The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet Pdf

This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642597213

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Discontinuous Galerkin Methods by Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu Pdf

A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Author : Philippe G. Clarlet
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:1405172153

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The Finite Element Method for Elliptic Problems by Philippe G. Clarlet Pdf

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 41,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Author : I. Galligani,E. Magenes
Publisher : Springer
Page : 371 pages
File Size : 41,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540371588

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Mathematical Aspects of Finite Element Methods by I. Galligani,E. Magenes Pdf

Author : Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 40,6 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9780387688053

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Numerical Approximation Methods for Elliptic Boundary Value Problems by Olaf Steinbach Pdf

This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.

Author : Alfio Quarteroni
Publisher : Springer Science & Business
Page : 658 pages
File Size : 42,7 Mb
Release : 2014-04-25
Category : Mathematics
ISBN : 9788847055223

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Numerical Models for Differential Problems by Alfio Quarteroni Pdf

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Author : Vidar Thomee
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 41,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662033593

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Galerkin Finite Element Methods for Parabolic Problems by Vidar Thomee Pdf

My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.

Author : B. Mercier
Publisher : Springer
Page : 212 pages
File Size : 54,6 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015049315909

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Lectures on Topics in Finite Element Solution of Elliptic Problems by B. Mercier Pdf

THESE NOTES SUMMARISE a course on the finite element solution of Elliptic problems, which took place in August 1978, in Bangalore. I would like to thank Professor Ramanathan without whom this course would not have been possible, and Dr. K. Balagangadharan who welcomed me in Bangalore. Mr. Vijayasundaram wrote these notes and gave them a much better form that what I would have been able to. Finally, I am grateful to all the people I met in Bangalore since they helped me to discover the smile of India and the depth of Indian civilization. Bertrand Mercier Paris, June 7, 1979. 1. SOBOLEV SPACES IN THIS CHAPTER the notion of Sobolev space Hl(n) is introduced. We state the Sobolev imbedding theorem, Rellich theorem, and Trace theorem for Hl(n), without proof. For the proof of the theorems the reader is r~ferred to ADAMS [1]. n 1. 1. NOTATIONS. Let n em (n = 1, ~ or 3) be an open set. Let r denote the boundary of 0, it is lSSlimed to be bounded and smooth. Let 2 2 L (n) = {f: Jlfl dx

Author : Andrei Maxim
Publisher : Unknown
Page : 224 pages
File Size : 51,8 Mb
Release : 2007
Category : Electronic
ISBN : CORNELL:31924108502679

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Aspects of the Finite Element Method for Elliptic Partial Differential Equations by Andrei Maxim Pdf

Author : Pavel B. Bochev,Max D. Gunzburger
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 55,6 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387689227

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Least-Squares Finite Element Methods by Pavel B. Bochev,Max D. Gunzburger Pdf

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Author : Bo-Nan Jiang
Publisher : Unknown
Page : 22 pages
File Size : 41,6 Mb
Release : 1991
Category : Finite element method
ISBN : UIUC:30112059174323

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Optimal Least-squares Finite Element Method for Elliptic Problems by Bo-Nan Jiang Pdf