Linear Convergence Of An Adaptive Finite Element Method For The P Laplacian Equation

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Multiscale, Nonlinear and Adaptive Approximation

Author : Ronald DeVore
Publisher : Springer Science & Business Media
ISBN 13 : 3642034136
Total Pages : 671 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Multiscale, Nonlinear and Adaptive Approximation by : Ronald DeVore

Download or read book Multiscale, Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer Science & Business Media. This book was released on 2009-09-16 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.

Numerical Approximation of Partial Differential Equations

Author : Sören Bartels
Publisher : Springer
ISBN 13 : 3319323547
Total Pages : 541 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Numerical Approximation of Partial Differential Equations by : Sören Bartels

Download or read book Numerical Approximation of Partial Differential Equations written by Sören Bartels and published by Springer. This book was released on 2016-06-02 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Advances in Mathematical Modeling, Optimization and Optimal Control

Author : Jean-Baptiste Hiriart-Urruty
Publisher : Springer
ISBN 13 : 3319307851
Total Pages : 205 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Advances in Mathematical Modeling, Optimization and Optimal Control by : Jean-Baptiste Hiriart-Urruty

Download or read book Advances in Mathematical Modeling, Optimization and Optimal Control written by Jean-Baptiste Hiriart-Urruty and published by Springer. This book was released on 2016-05-19 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.

Recent Advances in Partial Differential Equations and Applications

Author : Vicenţiu D. Rădulescu
Publisher : American Mathematical Soc.
ISBN 13 : 1470415216
Total Pages : 418 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Advances in Partial Differential Equations and Applications by : Vicenţiu D. Rădulescu

Download or read book Recent Advances in Partial Differential Equations and Applications written by Vicenţiu D. Rădulescu and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

Multiscale, Nonlinear and Adaptive Approximation

Author : Ronald DeVore
Publisher : Springer
ISBN 13 : 9783642424571
Total Pages : 0 pages
Book Rating : 4.4/5 (245 download)

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Book Synopsis Multiscale, Nonlinear and Adaptive Approximation by : Ronald DeVore

Download or read book Multiscale, Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer. This book was released on 2014-12-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . . . . . . . . . . . . . . . . . 7 7 Hyperbolic partial differential equations and conservation laws . . . 8 8 Engineering collaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 Thepresent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 Finalremarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Publications by Wolfgang Dahmen (as of summer 2009). . . . . . . . . . . . . . . 10 The way things were in multivariate splines: A personal view. . . . . . . . . . . 19 Carl de Boor 1 Tensor product spline interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Quasiinterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 MultivariateB-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Kergininterpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Meshless Methods and Their Numerical Properties

Author : Hua Li
Publisher : CRC Press
ISBN 13 : 1466517476
Total Pages : 429 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Meshless Methods and Their Numerical Properties by : Hua Li

Download or read book Meshless Methods and Their Numerical Properties written by Hua Li and published by CRC Press. This book was released on 2013-02-22 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the m

Multiscale and Adaptivity: Modeling, Numerics and Applications

Author : Silvia Bertoluzza
Publisher : Springer
ISBN 13 : 3642240798
Total Pages : 324 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Multiscale and Adaptivity: Modeling, Numerics and Applications by : Silvia Bertoluzza

Download or read book Multiscale and Adaptivity: Modeling, Numerics and Applications written by Silvia Bertoluzza and published by Springer. This book was released on 2012-01-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.

Optimization and Control for Partial Differential Equations

Author : Roland Herzog
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110696002
Total Pages : 386 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Optimization and Control for Partial Differential Equations by : Roland Herzog

Download or read book Optimization and Control for Partial Differential Equations written by Roland Herzog and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Automated Solution of Differential Equations by the Finite Element Method

Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models

Author : Tadele Mengesha
Publisher : Springer Nature
ISBN 13 : 3031340892
Total Pages : 325 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models by : Tadele Mengesha

Download or read book A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models written by Tadele Mengesha and published by Springer Nature. This book was released on 2023-09-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

Lebesgue and Sobolev Spaces with Variable Exponents

Author : Lars Diening
Publisher : Springer
ISBN 13 : 3642183638
Total Pages : 516 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening

Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

The Finite Element Method: Theory, Implementation, and Applications

Author : Mats G. Larson
Publisher : Springer Science & Business Media
ISBN 13 : 3642332870
Total Pages : 403 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson

Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

A Posteriori Error Estimation Techniques for Finite Element Methods

Author : Rüdiger Verfürth
Publisher : Oxford University Press
ISBN 13 : 0199679428
Total Pages : 414 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis A Posteriori Error Estimation Techniques for Finite Element Methods by : Rüdiger Verfürth

Download or read book A Posteriori Error Estimation Techniques for Finite Element Methods written by Rüdiger Verfürth and published by Oxford University Press. This book was released on 2013-04-18 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.

Space-Time Methods

Author : Ulrich Langer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110548488
Total Pages : 262 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Space-Time Methods by : Ulrich Langer

Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.

A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques

Author : Rüdiger Verführt
Publisher : Springer
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques by : Rüdiger Verführt

Download or read book A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques written by Rüdiger Verführt and published by Springer. This book was released on 1996-07 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Elements II

Author : Alexandre Ern
Publisher : Springer Nature
ISBN 13 : 3030569233
Total Pages : 491 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Finite Elements II by : Alexandre Ern

Download or read book Finite Elements II written by Alexandre Ern and published by Springer Nature. This book was released on 2021-04-22 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second 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 II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.

Verification and Validation in Scientific Computing

Author : William L. Oberkampf
Publisher : Cambridge University Press
ISBN 13 : 1139491768
Total Pages : 782 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Verification and Validation in Scientific Computing by : William L. Oberkampf

Download or read book Verification and Validation in Scientific Computing written by William L. Oberkampf and published by Cambridge University Press. This book was released on 2010-10-14 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.