Hybrid finite element approximation of elliptic boundary value problems
Author: Alfio Quarteroni
Publisher:
Published: 1979
Total Pages: 45
ISBN-13:
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Approximation of Elliptic Boundary-Value Problems
Author: Jean-Pierre Aubin
Publisher: Courier Corporation
Published: 2007-01-01
Total Pages: 386
ISBN-13: 0486457915
DOWNLOAD EBOOKA marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.
Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems
Author: Ivo Babuška
Publisher:
Published: 1977
Total Pages: 47
ISBN-13:
DOWNLOAD EBOOKMixed-hybrid finite element approximations of second-order elliptic boundary-value problems
Author: Ivo Babuška
Publisher:
Published: 1975
Total Pages: 47
ISBN-13:
DOWNLOAD EBOOKMixed-hybrid finite element approximations are described for second-order elliptic boundary-value problems in which independent approximations are used for the solution and its gradient on the interior of an element and the trace of the gradients on the boundary of the element. This leads to nonconforming finite elements. The independent boundary approximations are introduced by means of Lagrange multipliers. A-priori error estimates are derived. several other finite element models are also obtained as special cases. (Author).
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
DOWNLOAD EBOOKThis 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.
The Finite Element Method for Elliptic Problems
Author: Philippe G. Ciarlet
Publisher: SIAM
Published: 2002-04-01
Total Pages: 552
ISBN-13: 0898715148
DOWNLOAD EBOOKThis 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.
The Finite Element Method for Elliptic Problems
Author: P.G. Ciarlet
Publisher: Elsevier
Published: 1978-01-01
Total Pages: 551
ISBN-13: 0080875254
DOWNLOAD EBOOKThe 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.
Advanced Finite Element Methods and Applications
Author: Thomas Apel
Publisher: Springer Science & Business Media
Published: 2012-07-16
Total Pages: 380
ISBN-13: 3642303161
DOWNLOAD EBOOKThis volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.
Raising the Accuracy of Finite Element Approximations to Elliptic Boundary Value Problems
Author: Susanna Szabó
Publisher:
Published: 2001
Total Pages: 130
ISBN-13:
DOWNLOAD EBOOKFinite Element Solution of Boundary Value Problems
Author: O. Axelsson
Publisher: SIAM
Published: 1984-01-01
Total Pages: 455
ISBN-13: 9780898719253
DOWNLOAD EBOOKFinite Element Solution of Boundary Value Problems: Theory and Computation provides a thorough, balanced introduction to both the theoretical and the computational aspects of the finite element method for solving boundary value problems for partial differential equations. Although significant advances have been made in the finite element method since this book first appeared in 1984, the basics have remained the same, and this classic, well-written text explains these basics and prepares the reader for more advanced study. Useful as both a reference and a textbook, complete with examples and exercises, it remains as relevant today as it was when originally published. Audience: this book is written for advanced undergraduate and graduate students in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined practitioners in engineering and the physical sciences.
