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Constructive Methods For Elliptic Equations
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Book Synopsis Constructive Methods for Elliptic Equations by : R.P. Gilbert
Download or read book Constructive Methods for Elliptic Equations written by R.P. Gilbert and published by Springer. This book was released on 2006-11-15 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily these lectures are a report on recent work by the Indiana University group working on Function theoretic methods as applied to the theory of partial differential equations.
Book Synopsis Constructive Methods for Elliptic Equations by : R. P. Gilbert
Download or read book Constructive Methods for Elliptic Equations written by R. P. Gilbert and published by . This book was released on 2014-01-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constructive Methods for Elliptic Equations [By] Robert P. Gilbert by : Robert P. Gilbert
Download or read book Constructive Methods for Elliptic Equations [By] Robert P. Gilbert written by Robert P. Gilbert and published by . This book was released on 1974 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Methods and Numerical Analysis for Elliptic Complex Equation by : Guo Chun Wen
Download or read book Approximate Methods and Numerical Analysis for Elliptic Complex Equation written by Guo Chun Wen and published by CRC Press. This book was released on 1999-06-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods for elliptic partial differential equations have been the subject of many books in recent years, but few have treated the subject of complex equations. In this important new book, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiple connected domains. Constructive methods are systematically applied to proper boundary value problems which include very general boundary conditions. Approximate and numerical methods, such as the Newton imbedding method, the continuity method, the finite element method, the difference method and the boundary integral method, as well as their applications, are discussed in detail. The book will be of interest to all scientists studying the theory or applications of complex analysis.
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 and published by CRC Press. This book was released on 2018-05-04 with total page 379 pages. 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
Book Synopsis Direct Methods in the Theory of Elliptic Equations by : Jindrich Necas
Download or read book Direct Methods in the Theory of Elliptic Equations written by Jindrich Necas and published by Springer Science & Business Media. This book was released on 2011-10-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
Book Synopsis Constructive Methods for Determining the Solutions of Higher Order Elliptic Partial Differential Equations by : Dean Kenneth Kukral
Download or read book Constructive Methods for Determining the Solutions of Higher Order Elliptic Partial Differential Equations written by Dean Kenneth Kukral and published by . This book was released on 1972 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Wavelet Methods for Elliptic Partial Differential Equations by : Karsten Urban
Download or read book Wavelet Methods for Elliptic Partial Differential Equations written by Karsten Urban and published by OUP Oxford. This book was released on 2008-11-27 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of wavelets go back to the beginning of the last century and wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have, however, been used successfully in other areas, such as elliptic partial differential equations, which can be used to model many processes in science and engineering. This book, based on the author's course and accessible to those with basic knowledge of analysis and numerical mathematics, gives an introduction to wavelet methods in general and then describes their application for the numerical solution of elliptic partial differential equations. Recently developed adaptive methods are also covered and each scheme is complemented with numerical results, exercises, and corresponding software tools.
Book Synopsis Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities by : Zi Cai Li
Download or read book Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities written by Zi Cai Li and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.
Book Synopsis The Numerical Solution of Elliptic Equations by : Garrett Birkhoff
Download or read book The Numerical Solution of Elliptic Equations written by Garrett Birkhoff and published by SIAM. This book was released on 1971-01-01 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
Book Synopsis Direct Methods in the Theory of Elliptic Equations by : Jindrich Necas
Download or read book Direct Methods in the Theory of Elliptic Equations written by Jindrich Necas and published by Springer. This book was released on 2011-10-09 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
Book Synopsis Nonlinear Elliptic Equations and Nonassociative Algebras by : Nikolai Nadirashvili
Download or read book Nonlinear Elliptic Equations and Nonassociative Algebras written by Nikolai Nadirashvili and published by American Mathematical Soc.. This book was released on 2014-12-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.
Author :Marc Alexander Schweitzer Publisher :Springer Science & Business Media ISBN 13 :3642593259 Total Pages :197 pages Book Rating :4.6/5 (425 download)
Book Synopsis A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations by : Marc Alexander Schweitzer
Download or read book A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations written by Marc Alexander Schweitzer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.
Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
Book Synopsis Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators by : István Faragó
Download or read book Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators written by István Faragó and published by Nova Publishers. This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications
Book Synopsis Singularities and Constructive Methods for Their Treatment by : Pierre Grisvard
Download or read book Singularities and Constructive Methods for Their Treatment written by Pierre Grisvard and published by Springer. This book was released on 2006-11-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Marching Methods and Domain Decomposition by : Patrick J. Roache
Download or read book Elliptic Marching Methods and Domain Decomposition written by Patrick J. Roache and published by CRC Press. This book was released on 1995-06-29 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.
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