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Uniform In Varepsilon Convergence Of Finite Element Method For Convection Diffusion Equations Using A Priori Chosen Meshes
Download Uniform In Varepsilon Convergence Of Finite Element Method For Convection Diffusion Equations Using A Priori Chosen Meshes full books in PDF, epub, and Kindle. Read online Uniform In Varepsilon Convergence Of Finite Element Method For Convection Diffusion Equations Using A Priori Chosen Meshes ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Uniform in $ \varepsilon $ Convergence of Finite Element Method for Convection-diffusion Equations Using a Priori Chosen Meshes by : Mariana Nikolowa
Download or read book Uniform in $ \varepsilon $ Convergence of Finite Element Method for Convection-diffusion Equations Using a Priori Chosen Meshes written by Mariana Nikolowa and published by . This book was released on 1998 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems by : Torsten Linß
Download or read book Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems written by Torsten Linß and published by Springer. This book was released on 2009-11-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
Book Synopsis BEM-based Finite Element Approaches on Polytopal Meshes by : Steffen Weißer
Download or read book BEM-based Finite Element Approaches on Polytopal Meshes written by Steffen Weißer and published by Springer. This book was released on 2019-07-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Book Synopsis Uniformly Convergent Finite Element Methods for Singularly Perturbed Convection Diffusion Equations by : Willy Dörfler
Download or read book Uniformly Convergent Finite Element Methods for Singularly Perturbed Convection Diffusion Equations written by Willy Dörfler and published by . This book was released on 1998 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Principle in Finite Element Models for Convection-diffusion Phenomena by : Tsutomu Ikeda
Download or read book Maximum Principle in Finite Element Models for Convection-diffusion Phenomena written by Tsutomu Ikeda and published by North Holland. This book was released on 1983 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling & Data Analysis in Biotechnology & Medical Engineering
Book Synopsis Finite Element Methods by : Michel Krizek
Download or read book Finite Element Methods written by Michel Krizek and published by Routledge. This book was released on 2017-11-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.
Book Synopsis Moving Space-time Finite Element Methods for Convection-diffusion Problems by : Rafael Brigham Neves Ferreira Santos
Download or read book Moving Space-time Finite Element Methods for Convection-diffusion Problems written by Rafael Brigham Neves Ferreira Santos and published by . This book was released on 1991 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mesh Free Methods written by G.R. Liu and published by CRC Press. This book was released on 2002-07-29 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,
Book Synopsis Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems by : Torsten Lin y
Download or read book Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems written by Torsten Lin y and published by . This book was released on 2009-11-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on numerical methods for singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. A classification and a survey of layer-adapted meshes for reaction-convection-diffusion problems are included. This structured and comprehensive account of current ideas in the numerical analysis for various methods on layer-adapted meshes is addressed to researchers in finite element theory and perturbation problems. Finite differences, finite elements and finite volumes are all covered.
Book Synopsis Layer-adapted Meshes for Convection-diffusion Problems by :
Download or read book Layer-adapted Meshes for Convection-diffusion Problems written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on numerical methods for singular perturbation problems - in particular stationary convection-dominated convection-diffusion problems. More precisely it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. An early important contribution towards the optimization of numerical methods by means of special meshes was made by N.S. Bakhvalov in 1969. His paper spawned a lively discussion in the literature with a number of further meshes being proposed and applied to various singular perturbation problems. However, in the mid 1980s this development stalled, but was enlivend again by G.I. Shishkin's proposal of piecewise- equidistant meshes in the early 1990s. Because of their very simple structure they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on competing meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue. With this contribution we try to counter this development and lay the emphasis on more general meshes that - apart from performing better than piecewise-uniform meshes - provide a much deeper insight in the course of their analysis. In this monograph a classification and a survey are given of layer-adapted meshes for convection-diffusion problems. It tries to give a comprehensive review of state-of-the art techniques used in the convergence analysis for various numerical methods: finite differences, finite elements and finite volumes. While for finite difference schemes applied to one-dimensional problems a rather complete convergence theory for arbitrary meshes is developed, the theory is more fragmentary for other methods and problems and still requires the restriction to certain classes of meshes.
Book Synopsis Mesh Enhancement by : Glen A. Hansen
Download or read book Mesh Enhancement written by Glen A. Hansen and published by Imperial College Press. This book was released on 2005 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on mesh (grid) enhancement techniques ? specifically, the use of selected elliptic methods for both structured and unstructured meshes associated with computational physics applications. Mesh enhancement is the process in which an existing mesh is modified to better meet the requirements of the physics application. To provide the reader with sufficient background information, seven of the nine chapters contain a summary of the numerical simulation process, basic background on mesh terminology and generation approaches, computational geometry, discretization of differential equations, methods of solving linear and nonlinear algebraic systems, geometry of surfaces in Euclidean space, and general elliptic methods for mesh enhancement. Furthermore, these chapters use the concept of harmonic coordinates to develop a unifying framework, the Laplace-Beltrami system, which is the governing principle of the book. The final two chapters apply this scheme, along with other selected elliptic methods, to various structured and unstructured example problems.
Book Synopsis Moving Mesh Finite Element Method for Time Dependent Convection-Diffusion Problems by : Matthew Maxwell McCoy
Download or read book Moving Mesh Finite Element Method for Time Dependent Convection-Diffusion Problems written by Matthew Maxwell McCoy and published by . This book was released on 2021 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moving mesh finite element method (MM-FEM) has been a significant force in numerically approximating solutions to differential equations that otherwise exhibit spurious, artificial oscillations. This is especially true for singularly perturbed convection-diffusion problems. In the presence of vanishing molecular diffusivity, MM- FEM may not suffice. The numerical method may exhibit under-diffusive properties and other methods need to be integrated into the classic Galerkin formulation. We implement the so-called streamline upwind Petrov-Galerkin method into the adaptive moving mesh method. In particular, we investigate the computation of so-called enhanced diffusivity for spatiotemporal periodic turbulent flows. We look at the case of Brownian tracer particles, i.e. negligible inertial effects. These types of passive advection-diffusion models are used in atmospheric models with turbulent diffusion, so-called Benard-advection cells, and porous materials, along with many other areas of science and engineering. As molecular diffusivity decreases, interior and boundary layers propagate along the streamlines. Once spurious oscillations are present, they too will propagate along the streamlines. Thus, specialized numerical methods are needed in order to resolve these areas of the domain where large gradients are present. The discrete maximum principle is also investigated for general anisotropic time dependent convection-diffusion equations. We obtain lower and upper bounds for time steps as well as obtain conditions on the mass and stiffness matrices resulting from the SUPG formulation. Our approach depends on two meshes and taking into consideration two diffusion matrices and applying metric intersection.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781723205262 Total Pages :110 pages Book Rating :4.2/5 (52 download)
Book Synopsis Mesh Refinement in Finite Element Analysis by Minimization of the Stiffness Matrix Trace by : National Aeronautics and Space Administration (NASA)
Download or read book Mesh Refinement in Finite Element Analysis by Minimization of the Stiffness Matrix Trace written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-18 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution. Kittur, Madan G. and Huston, Ronald L. Unspecified Center ALGORITHMS; COMPUTATIONAL GRIDS; FINITE ELE...
Book Synopsis A Finite Element Formulation for the Numerical Solution of the Convection-diffusion Equation by : Ramon Codina
Download or read book A Finite Element Formulation for the Numerical Solution of the Convection-diffusion Equation written by Ramon Codina and published by . This book was released on 1993 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixed Finite Elements, Compatibility Conditions, and Applications by : Daniele Boffi
Download or read book Mixed Finite Elements, Compatibility Conditions, and Applications written by Daniele Boffi and published by Springer. This book was released on 2008-04-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.
Book Synopsis Uniformly Convergent Approximation On Special Meshes by : Özgür Bingöl
Download or read book Uniformly Convergent Approximation On Special Meshes written by Özgür Bingöl and published by . This book was released on 2007 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider finite difference methods for the approximation of one-dimensional convection-diffusion problem with a small parameter multiplying the diffusion term. An analysis of the centered difference and upwind difference schemes on equidistant meshes shows that these methods are not uniformly convergent in the discrete maximum norm. However, we show that the upwind method over a set of suitably distributed mesh points produce uniformly convergent approximations in the discrete maximum norm. We further investigate the upwind difference method for the approximation of the convection-diffusion problem with a point source. Theoretical findings are supported with the numerical results.
Book Synopsis Mesh Methods by : Viktor A. Rukavishnikov
Download or read book Mesh Methods written by Viktor A. Rukavishnikov and published by MDPI. This book was released on 2021-03-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
