Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem

Author: Roland Glowinski

Publisher: SIAM

Published: 2015-11-04

Total Pages: 473

ISBN-13: 1611973783

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Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.

The Finite Element Method for Elliptic Problems
The Finite Element Method for Elliptic Problems

Author: P.G. Ciarlet

Publisher: Elsevier

Published: 1978-01-01

Total Pages: 551

ISBN-13: 0080875254

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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.

Numerical Approximation Methods for Elliptic Boundary Value Problems
Numerical Approximation Methods for Elliptic Boundary Value Problems

Author: Olaf Steinbach

Publisher: Springer Science & Business Media

Published: 2007-12-22

Total Pages: 392

ISBN-13: 0387688056

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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.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Author: Peter Knabner

Publisher: Springer Science & Business Media

Published: 2003-06-26

Total Pages: 437

ISBN-13: 038795449X

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This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Solving Elliptic Problems Using ELLPACK
Solving Elliptic Problems Using ELLPACK

Author: John R. Rice

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 491

ISBN-13: 1461250188

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ELLP ACK is a many faceted system for solving elliptic partial differential equations. It is a forerunner of the very high level, problem solving environments or expert systems that will become common in the next decade. While it is still far removed from the goals of the future, it is also far advanced compared to the Fortran library approach in common current use. Many people will find ELLP ACK an easy way to solve simple or moderately complex elliptic problems. Others will be able to solve really hard problems by digging a little deeper into ELLP ACK. ELLP ACK is a research tool for the study of numerical methods for solving elliptic problems. Its original purpose was for the evaluation and comparison of numerical software for elliptic problems. Simple examples of this use are given in Chapters 9-11. The general conclusion is that there are many ways to solve most elliptic problems, there are large differences in their efficiency and the most common ways are often less efficient, sometimes dramatically so.

Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM
Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM

Author: John A. Trangenstein

Publisher: Cambridge University Press

Published: 2013-04-18

Total Pages: 657

ISBN-13: 0521877261

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For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Numerical Solution of Partial Differential Equations by the Finite Element Method
Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 290

ISBN-13: 0486131599

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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.

Elliptic Differential Equations
Elliptic Differential Equations

Author: W. Hackbusch

Publisher: Springer Science & Business Media

Published: 1992

Total Pages: 334

ISBN-13: 9783540548225

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Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR