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Numerical Approximation Methods for Elliptic Boundary Value Problems
Author: Olaf Steinbach
Publisher: Springer Science & Business Media
Published: 2007-11-26
Total Pages: 392
ISBN-13: 0387313125
DOWNLOAD EBOOK →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
Author: Peter Knabner
Publisher: Springer Science & Business Media
Published: 2006-05-26
Total Pages: 437
ISBN-13: 0387217622
DOWNLOAD EBOOK →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.
Numerical Analysis
Author: R. Teman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 170
ISBN-13: 9401025657
DOWNLOAD EBOOK →This book is an introduction to one of the important as pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation. This book is not a systematic study of the subject, but the methods developed here can be applied to large classes of linear and nonlinear elliptic problems. The book assumes that the reader's knowledge of Anal ysis is comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.
The Finite Element Method for Elliptic Problems
Author: P.G. Ciarlet
Publisher: Elsevier
Published: 1978-01-01
Total Pages: 551
ISBN-13: 0080875254
DOWNLOAD EBOOK →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.
Wavelet Methods — Elliptic Boundary Value Problems and Control Problems
Author: Angela Kunoth
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 150
ISBN-13: 332280027X
DOWNLOAD EBOOK →Diese Monographie spannt einen Bogen rund um die aktuelle Thematik Wavelets, um neueste Entwicklungen anhand aufeinander aufbauender Probleme darzustellen und das konzeptuelle Potenzial von Waveletmethoden für Partielle Differentialgleichungen zu demonstrieren.
Elliptic Boundary Value Problems on Corner Domains
Author: Monique Dauge
Publisher: Springer
Published: 2006-11-14
Total Pages: 266
ISBN-13: 3540459421
DOWNLOAD EBOOK →This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic theory (new approaches and results) as well as a synthesis of many already known results; those who need regularity conditions and descriptions of singularities for numerical analysis will find precise statements and also a means to obtain further one in many explicit situtations.
Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Author: Peter Knabner
Publisher: Springer Nature
Published: 2021-11-19
Total Pages: 811
ISBN-13: 3030793850
DOWNLOAD EBOOK →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.
Numerical Methods For Elliptic Problems With Singularities: Boundary Mtds And Nonconforming Combinatn
Author: Zi-cai Li
Publisher: World Scientific
Published: 1990-12-27
Total Pages: 280
ISBN-13: 981450680X
DOWNLOAD EBOOK →This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.
Partial Differential Equations with Numerical Methods
Author: Stig Larsson
Publisher: Springer Science & Business Media
Published: 2008-12-05
Total Pages: 263
ISBN-13: 3540887059
DOWNLOAD EBOOK →The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
