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hp-Finite Element Methods for Singular Perturbations

2004-10-19 Mathematics
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Release : 2004-10-19
Genre : Mathematics
Kind : eBook
Book Rating : 81X/5 ( reviews)

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Book Synopsis hp-Finite Element Methods for Singular Perturbations by : Jens M. Melenk

Download or read book hp-Finite Element Methods for Singular Perturbations written by Jens M. Melenk. This book was released on 2004-10-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Hp Version of the Finite Element Method for Singularly Perturbed Problems

1996 Boundary value problems
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Release : 1996
Genre : Boundary value problems
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis The Hp Version of the Finite Element Method for Singularly Perturbed Problems by : Christos Xenophontos

Download or read book The Hp Version of the Finite Element Method for Singularly Perturbed Problems written by Christos Xenophontos. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

p- and hp- Finite Element Methods

1998-10-15 Computers
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Release : 1998-10-15
Genre : Computers
Kind : eBook
Book Rating : 903/5 ( reviews)

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Book Synopsis p- and hp- Finite Element Methods by : C. Schwab

Download or read book p- and hp- Finite Element Methods written by C. Schwab. This book was released on 1998-10-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Robust Numerical Methods for Singularly Perturbed Differential Equations

2008-09-17 Mathematics
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Release : 2008-09-17
Genre : Mathematics
Kind : eBook
Book Rating : 675/5 ( reviews)

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Book Synopsis Robust Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos

Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos. This book was released on 2008-09-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 296/5 ( reviews)

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Book Synopsis Analyzing Multiscale Phenomena Using Singular Perturbation Methods by : Jane Cronin

Download or read book Analyzing Multiscale Phenomena Using Singular Perturbation Methods written by Jane Cronin. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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