Download or read book A Posteriori Error Estimation for Simulation of Diffusion and Fluid Mechanics Problems by Finite Volume Techniques written by Anh Ha Le and published by . This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce travail concerne les estimations a posteriori pour la simulation numérique, par des méthodes de volumes finis, de plusieurs modèles liés à la mécanique des fluides : le problème de Stokes stationnaire, l'équation de Darcy non-linéaire et l'équation de transport linéaire. De plus, un résultat concerant des inégalités de Poincaré discrètes sur des maillages bidimensionels quelconques est également présenté.
Download or read book A Posteriori Error Analysis Via Duality Theory written by Weimin Han and published by Springer Science & Business Media. This book was released on 2006-07-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Posteriori Error Estimation for Finite Volume Simulations of Fluid Flows written by Brian Van Straalen and published by . This book was released on 1995 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics written by J. Z. Zhu and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Review of Posteriori Error Estimation Adaptive Mesh Refinement Techniques written by Rudiger Verfurth and published by Wiley. This book was released on 1996-06-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical methods for the Navier Stokes equations written by Friedrich-Karl Hebeker and published by Springer-Verlag. This book was released on 2013-07-29 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Posteriori Error Analysis Via Duality Theory written by Weimin Han and published by Springer. This book was released on 2004-11-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book A Posteriori Error Estimation for Finite Element Approximations of Fractional Laplacian Problems and Applications to Poro elasticity written by Raphaël Bulle and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript is concerned with a posteriori error estimation for the finiteelement discretization of standard and fractional partial differential equationsas well as an application of fractional calculus to the modeling of thehuman meniscus by poro-elasticity equations.In the introduction, we give an overview of the literature about a posteriori errorestimation for finite element methods and about adaptive mesh refinement methods.We also review the literature about fractional partial differential equationsand Caputo's fractional derivative with anomalous diffusion applications.We emphasize on the state-of-the-art of the Bank-Weiser estimator and of aposteriori error estimation for the spectral fractional Laplacian.The rest of the manuscript is organized as follows.The Chapter 1 is concerned with a proof of the reliability of theBank-Weiser estimator for three-dimensional problems discretized with linearLagrange finite elements. This result is an extension of a previous result fromthe literature.In Chapter 2 we present a numerical study of the Bank-Weiserestimator.We provide a novel implementation of the estimator in the FEniCS finiteelement software and working in parallel.We apply our code to a variety of elliptic equations, several differenttwo-dimensional Poisson problems and a three-dimensional linear elasticityproblem.In particular, we use our implementation into an adaptive mesh refinement method anda goal-oriented error estimation method.In addition we provide convergence studies for these methods as well as atimescale study of our error estimation method when performed in parallel.In Chapter 3 we derive a novel a posteriori estimator for theL2 error induced by the finite element discretization of the fractionalLaplacian operator.We provide an implementation of our method in the FEniCS finite elementsoftware.We apply our estimator to an adaptive refinement method for two-dimensional andthree-dimensional fractional Poisson equations.In addition, we provide numerical results on the convergence of this method.In Chapter 4 we present new theoretical results on theconvergence of a rational approximation method with consequences on theapproximation of fractional norms and a priori error estimation of the semi-discretization of the spectral fractional Laplacian.Finally, in Chapter 5 we provide an application of fractionalcalculus to the study of the human meniscus via poro-elasticity equations and the Caputo derivative.
Download or read book Reactive Flows Diffusion and Transport written by Willi Jäger and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume summarize the research results obtained in the former SFB 359 "Reactive Flow, Diffusion and Transport" which has been supported by the DFG over the period 1993-2004. The main subjects are physical-chemical processes sharing the difficulty of interacting diffusion, transport and reaction which cannot be considered separately. The modeling and simulation within this book is accompanied by experiments.
Download or read book Acta Numerica 2001 Volume 10 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2001-08-23 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical analysis and scientific computing.
Download or read book A Posteriori Error Estimates and Adaptive Solution of Fluid Flow Problems written by Bruno D. Welfert and published by . This book was released on 1990 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Filtration in Porous Media and Industrial Application written by M.S. Espedal and published by Springer. This book was released on 2007-05-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.
Download or read book Hemodynamical Flows written by Giovanni P. Galdi and published by Springer Science & Business Media. This book was released on 2008-04-17 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.
Download or read book Numerical Mathematics and Advanced Applications written by Miloslav Feistauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.
Download or read book Data driven modeling and optimization in fluid dynamics From physics based to machine learning approaches written by Michel Bergmann and published by Frontiers Media SA. This book was released on 2023-01-05 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
