Pointwise A Posteriori Error Estimates For Monotone Semi Linear Equations
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Pointwise A Posteriori Error Estimates For Monotone Semi Linear Equations
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Author :
language : en
Publisher:
Release Date : 2005
Pointwise A Posteriori Error Estimates For Monotone Semi Linear Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Residual Type A Posteriori Error Estimates For Semi Linear Parabolic Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 2010
Residual Type A Posteriori Error Estimates For Semi Linear Parabolic Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Differential equations categories.
A posteriori error analysis is the key idea for adaptive finite element methods for solving partial differential equations(PDEs). In this thesis, we are interested in a posteriori error analysis for semi-linear parabolic PDEs over polygonal domain in 2-D with Dirichlet boundary condition. We showed the efficiency and reliability of a posteriori error estimator by deriving the upper and local lower bounds based on the standard residual estimator under the assumption that the nonlinear function f is Lipschitz with respect to the variable u. We also constructed an algorithm for adaptive finite element method based on a posterior error estimations.
Boundary And Interior Layers Computational And Asymptotic Methods Bail 2016
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Author : Zhongyi Huang
language : en
Publisher: Springer
Release Date : 2017-10-26
Boundary And Interior Layers Computational And Asymptotic Methods Bail 2016 written by Zhongyi Huang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Mathematics categories.
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.
Boundary And Interior Layers Computational And Asymptotic Methods Bail 2018
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Author : Gabriel R. Barrenechea
language : en
Publisher: Springer Nature
Release Date : 2020-08-11
Boundary And Interior Layers Computational And Asymptotic Methods Bail 2018 written by Gabriel R. Barrenechea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Mathematics categories.
This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.
Pointwise A Posteriori Error Estimates For The Stokes Equations In Polyhedral Domains
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Author : Erik D. Svensson
language : en
Publisher:
Release Date : 2006
Pointwise A Posteriori Error Estimates For The Stokes Equations In Polyhedral Domains written by Erik D. Svensson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Multiscale And Adaptivity Modeling Numerics And Applications
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Author : Silvia Bertoluzza
language : en
Publisher: Springer
Release Date : 2012-01-06
Multiscale And Adaptivity Modeling Numerics And Applications written by Silvia Bertoluzza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.
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.
Error Estimates For Well Balanced Schemes On Simple Balance Laws
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Author : Debora Amadori
language : en
Publisher: Springer
Release Date : 2015-10-23
Error Estimates For Well Balanced Schemes On Simple Balance Laws written by Debora Amadori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Mathematics categories.
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
A Posteriori Error Analysis In Finite Element Approximation For Fully Discrete Semilinear Parabolic Problems
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Author : Younis Abid Abid Sabawi
language : en
Publisher:
Release Date : 2019
A Posteriori Error Analysis In Finite Element Approximation For Fully Discrete Semilinear Parabolic Problems written by Younis Abid Abid Sabawi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Computers categories.
This Chapter aims to investigate the error estimation of numerical approximation to a class of semilinear parabolic problems. More specifically, the time discretization uses the backward Euler Galerkin method and the space discretization uses the finite element method for which the meshes are allowed to change in time. The key idea in our analysis is to adapt the elliptic reconstruction technique, introduced by Makridakis and Nochetto 2003, enabling us to use the a posteriori error estimators derived for elliptic models and to obtain optimal order in L,àûH1 for Lipschitz and non-Lipschitz nonlinearities. In this Chapter, some challenges will be addressed to deal with nonlinear term by employing a continuation argument.
Adaptive Finite Element Methods For Differential Equations
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Author : Wolfgang Bangerth
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Adaptive Finite Element Methods For Differential Equations written by Wolfgang Bangerth and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.