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Author : Mathon, R
Release : 1972
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis On the Approximation of Elliptic Boundary Value Problems by Fundamental Solutions by : Mathon, R
Download or read book On the Approximation of Elliptic Boundary Value Problems by Fundamental Solutions written by Mathon, R. This book was released on 1972. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Pierre Aubin
Release : 2007-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 915/5 ( reviews)
Book Synopsis Approximation of Elliptic Boundary-Value Problems by : Jean-Pierre Aubin
Download or read book Approximation of Elliptic Boundary-Value Problems written by Jean-Pierre Aubin. This book was released on 2007-01-01. Available in PDF, EPUB and Kindle. Book excerpt: A 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.
Author : Olaf Steinbach
Release : 2007-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 056/5 ( reviews)
Book Synopsis Numerical Approximation Methods for Elliptic Boundary Value Problems by : Olaf Steinbach
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach. This book was released on 2007-12-22. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Christopher R. Mills
Release : 2009
Genre : Boundary value problems
Kind : eBook
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Book Synopsis Method of Approximate Fundamental Solutions for Ill-posed Elliptic Boundary Value Problems by : Christopher R. Mills
Download or read book Method of Approximate Fundamental Solutions for Ill-posed Elliptic Boundary Value Problems written by Christopher R. Mills. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eugene G. D'yakonov
Release : 2018-05-04
Genre : Mathematics
Kind : eBook
Book Rating : 66X/5 ( reviews)
Book Synopsis Optimization in Solving Elliptic Problems by : Eugene G. D'yakonov
Download or read book Optimization in Solving Elliptic Problems written by Eugene G. D'yakonov. This book was released on 2018-05-04. Available in PDF, EPUB and Kindle. Book excerpt: Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema
