Hp Finite Element Methods For Singular Perturbations

Author : Jens M. Melenk
Publisher : Springer
Page : 326 pages
File Size : 47,7 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540457817

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hp-Finite Element Methods for Singular Perturbations by Jens M. Melenk Pdf

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 : Leszek Demkowicz
Publisher : CRC Press
Page : 428 pages
File Size : 45,7 Mb
Release : 2006-10-25
Category : Mathematics
ISBN : 9781420011685

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Computing with hp-ADAPTIVE FINITE ELEMENTS by Leszek Demkowicz Pdf

Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementat

Author : Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publisher : Springer
Page : 428 pages
File Size : 48,7 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9783030142445

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Advanced Finite Element Methods with Applications by Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach Pdf

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Author : Vít Dolejší,Georg May
Publisher : Springer Nature
Page : 258 pages
File Size : 42,7 Mb
Release : 2022-06-06
Category : Mathematics
ISBN : 9783031042799

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Anisotropic hp-Mesh Adaptation Methods by Vít Dolejší,Georg May Pdf

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

Author : Jichun Li,Yi-Tung Chen
Publisher : CRC Press
Page : 423 pages
File Size : 48,9 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9780429556531

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Computational Partial Differential Equations Using MATLAB® by Jichun Li,Yi-Tung Chen Pdf

In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.

Author : Ivan G. Graham,Thomas Y. Hou,Omar Lakkis,Robert Scheichl
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 40,7 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783642220616

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Numerical Analysis of Multiscale Problems by Ivan G. Graham,Thomas Y. Hou,Omar Lakkis,Robert Scheichl Pdf

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Author : Yong Shi,Haohuan Fu,Yingjie Tian,Valeria V. Krzhizhanovskaya,Michael Harold Lees,Jack Dongarra,Peter M. A. Sloot
Publisher : Springer
Page : 884 pages
File Size : 43,9 Mb
Release : 2018-06-11
Category : Computers
ISBN : 9783319937014

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Computational Science – ICCS 2018 by Yong Shi,Haohuan Fu,Yingjie Tian,Valeria V. Krzhizhanovskaya,Michael Harold Lees,Jack Dongarra,Peter M. A. Sloot Pdf

The three-volume set LNCS 10860, 10861 and 10862 constitutes the proceedings of the 18th International Conference on Computational Science, ICCS 2018, held in Wuxi, China, in June 2018. The total of 155 full and 66 short papers presented in this book set was carefully reviewed and selected from 404 submissions. The papers were organized in topical sections named: Part I: ICCS Main Track Part II: Track of Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Track of Agent-Based Simulations, Adaptive Algorithms and Solvers; Track of Applications of Matrix Methods in Artificial Intelligence and Machine Learning; Track of Architecture, Languages, Compilation and Hardware Support for Emerging ManYcore Systems; Track of Biomedical and Bioinformatics Challenges for Computer Science; Track of Computational Finance and Business Intelligence; Track of Computational Optimization, Modelling and Simulation; Track of Data, Modeling, and Computation in IoT and Smart Systems; Track of Data-Driven Computational Sciences; Track of Mathematical-Methods-and-Algorithms for Extreme Scale; Track of Multiscale Modelling and Simulation Part III: Track of Simulations of Flow and Transport: Modeling, Algorithms and Computation; Track of Solving Problems with Uncertainties; Track of Teaching Computational Science; Poster Papers

Author : Valarmathi Sigamani,John J. H. Miller,Shivaranjani Nagarajan,Parthiban Saminathan
Publisher : Springer Nature
Page : 218 pages
File Size : 42,6 Mb
Release : 2022-01-24
Category : Mathematics
ISBN : 9789811675461

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Differential Equations and Applications by Valarmathi Sigamani,John J. H. Miller,Shivaranjani Nagarajan,Parthiban Saminathan Pdf

This book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system.

Author : Karl Kunisch,Günther Of,Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 825 pages
File Size : 47,8 Mb
Release : 2008-09-19
Category : Mathematics
ISBN : 9783540697770

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Numerical Mathematics and Advanced Applications by Karl Kunisch,Günther Of,Olaf Steinbach Pdf

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.

Author : Ulrich Langer,Peter Paule
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 49,5 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9783709107942

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Numerical and Symbolic Scientific Computing by Ulrich Langer,Peter Paule Pdf

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Author : Stefan Teufel
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 53,9 Mb
Release : 2003
Category : Perturbation (Quantum dynamics)
ISBN : 3540407235

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Adiabatic Perturbation Theory in Quantum Dynamics by Stefan Teufel Pdf

Author : Wolfgang Hackbusch
Publisher : Springer
Page : 455 pages
File Size : 47,7 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783662549612

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Elliptic Differential Equations by Wolfgang Hackbusch Pdf

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Author : Christian Grossmann,Hans-G. Roos,Martin Stynes
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 43,8 Mb
Release : 2007-10-04
Category : Mathematics
ISBN : 9783540715825

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Numerical Treatment of Partial Differential Equations by Christian Grossmann,Hans-G. Roos,Martin Stynes Pdf

This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.

Author : Zhongyi Huang,Martin Stynes,Zhimin Zhang
Publisher : Springer
Page : 211 pages
File Size : 46,8 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9783319672021

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Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016 by Zhongyi Huang,Martin Stynes,Zhimin Zhang Pdf

This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed differential equations; that is, problems whose solutions exhibit boundary and/or interior layers.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 122 pages
File Size : 48,5 Mb
Release : 2007
Category : Electronic
ISBN : 9783540737049

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Entropy Methods for the Boltzmann Equation by Anonim Pdf