Numerical Approximation Methods for Elliptic Boundary Value Problems
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 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.

Approximation of Elliptic Boundary-Value Problems
Approximation of Elliptic Boundary-Value Problems

Author: Jean-Pierre Aubin

Publisher: Courier Corporation

Published: 2007-01-01

Total Pages: 386

ISBN-13: 0486457915

DOWNLOAD EBOOK

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.

Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics
Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

Author: Victor A. Sadovnichiy

Publisher: Springer Nature

Published: 2020-11-24

Total Pages: 525

ISBN-13: 303050302X

DOWNLOAD EBOOK

This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

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

Computational Methods
Computational Methods

Author: G.R. Liu

Publisher: Springer Science & Business Media

Published: 2007-05-26

Total Pages: 954

ISBN-13: 1402039530

DOWNLOAD EBOOK

The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.

The Cauchy Problem for Solutions of Elliptic Equations
The Cauchy Problem for Solutions of Elliptic Equations

Author: Nikolai N. Tarkhanov

Publisher: Wiley-VCH

Published: 1995-05-23

Total Pages: 479

ISBN-13: 9783527400584

DOWNLOAD EBOOK

The book is an attempt to bring together various topics in partial differential equations related to the Cauchy problem for solutions of an elliptic equation. Ever since Hadamard, the Cauchy problem for solutions of elliptic equations has been known to be ill-posed. It is conditionally stable, just as is the case for even the simplest problems of analytic continuation of functions given on a subset of the boundary. (Such problems of analytic continuation served as a paradigm for the treatment here.) The study of the Cauchy problem is carried out in three directions: determining the degree of instability, which is connected with sharp theorems on approximation by solutions of an elliptic equation; finding solvability conditions, which is based on the development of Hilbert space methods in the Cauchy problem; and reconstructing solutions via their Cauchy data, which requires efficient ways of approximation. A wide range of topics is touched upon, among them are function spaces on compact sets, boundedness theorems for pseudodifferential operators in nonlocal spaces, nonlinear capacity and removable singularities, fundamental solutions, capacitary criteria for approximation by solutions of elliptic equations, and weak boundary values of the solutions. The theory applies as well to the Cauchy problem for solution of overdetermined elliptic systems.