Adaptive Finite Elements In The Discretization Of Parabolic Problems

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Adaptive Finite Elements in the Discretization of Parabolic Problems

Author : Christian A. Möller
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832528156
Total Pages : 259 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Adaptive Finite Elements in the Discretization of Parabolic Problems by : Christian A. Möller

Download or read book Adaptive Finite Elements in the Discretization of Parabolic Problems written by Christian A. Möller and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.

Galerkin Finite Element Methods for Parabolic Problems

Author : Vidar Thomee
Publisher : Springer Science & Business Media
ISBN 13 : 3662033593
Total Pages : 310 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomee

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.

Galerkin Finite Element Methods for Parabolic Problems

Author : Vidar Thomée
Publisher : Springer Science & Business Media
ISBN 13 : 9783540632368
Total Pages : 320 pages
Book Rating : 4.6/5 (323 download)

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Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomée

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomée and published by Springer Science & Business Media. This book was released on 2010 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems

Author : Jens Lang
Publisher : Springer Science & Business Media
ISBN 13 : 3662044846
Total Pages : 161 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems by : Jens Lang

Download or read book Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems written by Jens Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.

Advanced Finite Element Methods with Applications

Author : Thomas Apel
Publisher : Springer
ISBN 13 : 3030142442
Total Pages : 428 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Advanced Finite Element Methods with Applications by : Thomas Apel

Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Space-Time Methods

Author : Ulrich Langer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110548488
Total Pages : 261 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 261 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.

Design of Adaptive Finite Element Software

Author : Alfred Schmidt
Publisher : Springer Science & Business Media
ISBN 13 : 3540271562
Total Pages : 329 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Design of Adaptive Finite Element Software by : Alfred Schmidt

Download or read book Design of Adaptive Finite Element Software written by Alfred Schmidt and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.

Computing with hp-ADAPTIVE FINITE ELEMENTS

Author : Leszek Demkowicz
Publisher : CRC Press
ISBN 13 : 1420011693
Total Pages : 437 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Computing with hp-ADAPTIVE FINITE ELEMENTS by : Leszek Demkowicz

Download or read book Computing with hp-ADAPTIVE FINITE ELEMENTS written by Leszek Demkowicz and published by CRC Press. This book was released on 2007-11-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the

Numerical Solution of Partial Differential Equations by the Finite Element Method

Author : Claes Johnson
Publisher : Courier Corporation
ISBN 13 : 0486131599
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson

Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Mathematical Aspects of Finite Elements in Partial Differential Equations

Author : Carl de Boor
Publisher : Academic Press
ISBN 13 : 1483268071
Total Pages : 431 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Mathematical Aspects of Finite Elements in Partial Differential Equations by : Carl de Boor

Download or read book Mathematical Aspects of Finite Elements in Partial Differential Equations written by Carl de Boor and published by Academic Press. This book was released on 2014-05-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method. Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

Galerkin Finite Element Methods for Parabolic Problems

Author : V. Thomee
Publisher :
ISBN 13 : 9783662179895
Total Pages : 248 pages
Book Rating : 4.1/5 (798 download)

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Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : V. Thomee

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by V. Thomee and published by . This book was released on 2014-01-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Mathematics and Advanced Applications

Author : Karl Kunisch
Publisher : Springer Science & Business Media
ISBN 13 : 3540697772
Total Pages : 825 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Numerical Mathematics and Advanced Applications by : Karl Kunisch

Download or read book Numerical Mathematics and Advanced Applications written by Karl Kunisch and published by Springer Science & Business Media. This book was released on 2008-09-19 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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:

Hemodynamical Flows

Author : Giovanni P. Galdi
Publisher : Springer Science & Business Media
ISBN 13 : 3764378050
Total Pages : 512 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Hemodynamical Flows by : Giovanni P. Galdi

Download or read book Hemodynamical Flows written by Giovanni P. Galdi and published by Springer Science & Business Media. This book was released on 2008-03-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys research results on the physical and mathematical modeling, as well as the numerical simulation of complex fluid and structural mechanical processes occurring in the human blood circulation system. Topics treated include continuum mechanical description; choice of suitable liquid and wall models; mathematical analysis of coupled models; numerical methods for flow simulation; parameter identification and model calibration; fluid-solid interaction; mathematical analysis of piping systems; particle transport in channels and pipes; artificial boundary conditions, and many more. The book was developed from lectures presented by the authors at the Oberwolfach Research Institute (MFO), in Oberwolfach-Walke, Germany, November, 2005.

Modeling, Simulation and Optimization of Complex Processes

Author : Hans Georg Bock
Publisher : Springer Science & Business Media
ISBN 13 : 3642257070
Total Pages : 328 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Modeling, Simulation and Optimization of Complex Processes by : Hans Georg Bock

Download or read book Modeling, Simulation and Optimization of Complex Processes written by Hans Georg Bock and published by Springer Science & Business Media. This book was released on 2012-02-03 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains a selection of papers presented at the Fourth International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 2-6, 2009. The conference was organized by the Hanoi Institute of Mathematics, the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, mechanics, biology and medicine, engineering, hydrology problems, transport, communication networks, production scheduling, industrial and commercial problems.

Commutability of Gamma-limits in problems with multiple scales

Author : Martin Jesenko
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 383254478X
Total Pages : 145 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Commutability of Gamma-limits in problems with multiple scales by : Martin Jesenko

Download or read book Commutability of Gamma-limits in problems with multiple scales written by Martin Jesenko and published by Logos Verlag Berlin GmbH. This book was released on 2017-05-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.

Domain Decomposition Methods in Science and Engineering XXVI

Author : Susanne C. Brenner
Publisher : Springer Nature
ISBN 13 : 3030950255
Total Pages : 778 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Domain Decomposition Methods in Science and Engineering XXVI by : Susanne C. Brenner

Download or read book Domain Decomposition Methods in Science and Engineering XXVI written by Susanne C. Brenner and published by Springer Nature. This book was released on 2023-03-15 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.