Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 10
Book Description
A Posteriori Error Estimation Via Nonlinear Error Transport
Author: Numerical Error Estimation for Nonlinear Hyperbolic PDEs Via Nonlinear Error Transport
Author: A Posteriori Error Estimation for Nonlinear Problems by Duality Techniques
Author: Eberhard BänschA Posteriori Error Analysis Via Duality Theory
Author: Weimin HanPublisher: Springer Science & Business Media
ISBN: 038723537X
Category : Mathematics
Languages : en
Pages : 312
Book Description
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
Recent Advances in Scientific Computing and Applications
Author: Jichun LiPublisher: American Mathematical Soc.
ISBN: 0821887378
Category : Mathematics
Languages : en
Pages : 397
Book Description
This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.
A Review of Posteriori Error Estimation & Adaptive Mesh-Refinement Techniques
Author: Rudiger VerfurthPublisher: Wiley
ISBN: 9780471967958
Category : Mathematics
Languages : en
Pages : 134
Book Description
Wiley—Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Rüdiger Verfürth Ruhr-Universität Bochum, Germany Self-adaptive discretization methods have gained an enormous importance for the numerical solution of partial differential equations which arise in physical and technical applications. The aim of these methods is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools utilised are a posteriori error estimators and indicators which are able to give global and local information on the error of the numerical solution, using only the computed numerical solution and known data of the problem. Presenting the most frequently used error estimators which have been developed by various scientists in the last two decades, this book demonstrates that they are all based on the same basic principles. These principles are then used to develop an abstract framework which is able to handle general nonlinear problems. The abstract results are applied to various classes of nonlinear elliptic partial differential equations from, for example, fluid and continuum mechanics, to yield reliable and easily computable error estimators. The book covers stationary problems but omits transient problems, where theory is often still too complex and not yet well developed.
POD-based A-posteriori Error Estimation for Control Problems Governed by Nonlinear PDEs
Author: Stefan TrenzA Posteriori Error Estimates for Variable Time-step Discretizations of Nonlinear Equations
Author: A Posteriori Error Analysis Via Duality Theory
Author: Weimin HanPublisher: Springer
ISBN: 9780387235363
Category : Mathematics
Languages : en
Pages : 302
Book Description
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
A Posteriori Error Estimation with Finite Element Method of Lines for a Nonlinear Parabolic Equation in One Space Dimension
Author: Thanh TranPublisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 16
Book Description