Numerical Methods For Elliptic Problems With Singularities

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Numerical Methods For Elliptic Problems With Singularities

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Author : Zi-Cai Li
language : en
Publisher: World Scientific
Release Date : 1990

Numerical Methods For Elliptic Problems With Singularities written by Zi-Cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

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.

Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn

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Author : Zi-cai Li
language : en
Publisher: World Scientific
Release Date : 1990-12-27

Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn written by Zi-cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-27 with Mathematics categories.

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.

Combined Methods For Elliptic Equations With Singularities Interfaces And Infinities

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Author : Zi Cai Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Combined Methods For Elliptic Equations With Singularities Interfaces And Infinities written by Zi Cai Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

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.

Graded Finite Element Methods For Elliptic Problems In Nonsmooth Domains

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Author : Hengguang Li
language : en
Publisher: Springer Nature
Release Date : 2022-09-01

Graded Finite Element Methods For Elliptic Problems In Nonsmooth Domains written by Hengguang Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Mathematics categories.

This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.

Trefftz And Collocation Methods

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Author : Z-C. Li
language : en
Publisher: WIT Press
Release Date : 2008-02-22

Trefftz And Collocation Methods written by Z-C. Li and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-22 with Technology & Engineering categories.

This title was reviewed in the January 2009 issue of Mathematical Reviews.

Numerical Mathematics And Advanced Applications Enumath 2013

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Author : Assyr Abdulle
language : en
Publisher: Springer
Release Date : 2014-11-25

Numerical Mathematics And Advanced Applications Enumath 2013 written by Assyr Abdulle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Computers categories.

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

Progress In Industrial Mathematics At Ecmi 2008

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Author : Alistair D. Fitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23

Progress In Industrial Mathematics At Ecmi 2008 written by Alistair D. Fitt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.

The 15th European Conference on Mathematics for Industry was held in the agreeable surroundings of University College London, just 5 minutes walk from the British Museum in the heart of London, over the ?ve warm, sunny days from 30 June to 4 July 2008. Participants from all over the world met with the commonaimofreinforcingthe roleofmathematics asanoverarching resource for industry and business. The conference attracted over 300 participants from 30 countries, most of them participating with either a contributed talk, a minisymposium pres- tation or a plenary lecture. ‘Mathematics in Industry’ was interpreted in its widest sense as can be seen from the range of applications and techniques described in this volume. We mention just two examples. The Alan Tayler Lecture was given by Mario Primicerio on a problem arising from moving oil through pipelines when temperature variations a?ect the shearing properties of wax and thus modify the ?ow. The Wacker Prize winner, Master’s student Lauri Harhanen from the Helsinki University of Technology, showed how a novel piece of mathematics allowed new software to capture real-time images of teeth from the data supplied by present day dental machinery (see ECMI Newsletter 44). The meeting was attended by leading ?gures from government, bu- ness and science who all shared the same aim – to promote the application of innovative mathematics to industry, and identify industrial sectors that o?er the most exciting opportunities for mathematicians to provide new insight and new ideas.

Conference On Applications Of Numerical Analysis

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Author : John L. Morris
language : en
Publisher: Springer
Release Date : 2006-11-15

Conference On Applications Of Numerical Analysis written by John L. Morris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Numerical Analysis

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Author : D.F. Griffiths
language : en
Publisher: Springer
Release Date : 2006-12-08

Numerical Analysis written by D.F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

Scientific Computing In Electrical Engineering

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Author : Angelo Marcello Anile
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-10

Scientific Computing In Electrical Engineering written by Angelo Marcello Anile and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-10 with Technology & Engineering categories.

This book is a collection of papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sicily, in 2004. The series of SCEE conferences aims at addressing mathematical problems which have a relevancy to industry. The areas covered at SCEE-2004 were: Electromagnetism, Circuit Simulation, Coupled Problems and General mathematical and computational methods.