The Hp Version Of The Finite Element Method For Singularly Perturbed Problems
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Author | : Jens M. Melenk |
Publisher | : Springer |
Total Pages | : 331 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 354045781X |
Download hp-Finite Element Methods for Singular Perturbations Book in PDF, Epub and Kindle
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Author | : Christos Xenophontos |
Publisher | : |
Total Pages | : 278 |
Release | : 1996 |
Genre | : Boundary value problems |
ISBN | : |
Download The Hp Version of the Finite Element Method for Singularly Perturbed Problems Book in PDF, Epub and Kindle
Author | : C. Schwab |
Publisher | : Clarendon Press |
Total Pages | : 386 |
Release | : 1998-10-15 |
Genre | : Computers |
ISBN | : 9780198503903 |
Download p- and hp- Finite Element Methods Book in PDF, Epub and Kindle
The finite element method (FEM) is a numerical procedure for solving differential equations. Ever-increasing computing power means that engineers and applied mathematicians are seeking more complicated and sophisticated numerical methods to obtain progressively more accurate answers to problems in solid and fluid mechanics. The p- and hp- finite element methods are just such methods, and are therefore of great current interest. This book is the first to cover comprehensively the mathematical underpinnings of hp-FEM in one and two dimensions and pays particular attention to its applications in engineering.
Author | : Hans-Görg Roos |
Publisher | : Springer Science & Business Media |
Total Pages | : 599 |
Release | : 2008-09-17 |
Genre | : Mathematics |
ISBN | : 3540344675 |
Download Robust Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, Epub and Kindle
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Author | : |
Publisher | : |
Total Pages | : 836 |
Release | : 1994 |
Genre | : Aeronautics |
ISBN | : |
Download Scientific and Technical Aerospace Reports Book in PDF, Epub and Kindle
Author | : Jane Cronin |
Publisher | : American Mathematical Soc. |
Total Pages | : 201 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809296 |
Download Analyzing Multiscale Phenomena Using Singular Perturbation Methods Book in PDF, Epub and Kindle
To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
Author | : Alexandre Ern |
Publisher | : Springer Nature |
Total Pages | : 417 |
Release | : 2021-03-29 |
Genre | : Mathematics |
ISBN | : 3030573486 |
Download Finite Elements III Book in PDF, Epub and Kindle
This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.
Author | : Gunilla Kreiss |
Publisher | : Springer Science & Business Media |
Total Pages | : 900 |
Release | : 2010-10-19 |
Genre | : Mathematics |
ISBN | : 3642117953 |
Download Numerical Mathematics and Advanced Applications 2009 Book in PDF, Epub and Kindle
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Author | : Vít Dolejší |
Publisher | : Springer |
Total Pages | : 575 |
Release | : 2015-07-17 |
Genre | : Mathematics |
ISBN | : 3319192671 |
Download Discontinuous Galerkin Method Book in PDF, Epub and Kindle
The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Author | : Claudio Canuto |
Publisher | : Springer Science & Business Media |
Total Pages | : 585 |
Release | : 2007-09-23 |
Genre | : Science |
ISBN | : 3540307265 |
Download Spectral Methods Book in PDF, Epub and Kindle
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.