Adaptive Streamline Diffusion Finite Element Methods For Time Dependent Convection Diffusion Problems
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Adaptive Streamline Diffusion Finite Element Methods For Time Dependent Convection Diffusion Problems
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Author : Kenneth Eriksson
language : en
Publisher:
Release Date : 1993
Adaptive Streamline Diffusion Finite Element Methods For Time Dependent Convection Diffusion Problems written by Kenneth Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Adaptive Streamline Difusion Finite Element Methods For Time Dependent Convection Diffusion Problems
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Author : K. Eriksson
language : en
Publisher:
Release Date : 1993
Adaptive Streamline Difusion Finite Element Methods For Time Dependent Convection Diffusion Problems written by K. Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Adaptive Streamline Diffusion Finite Element Methods For Convection Diffusion Problems
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Author : Kenneth Eriksson
language : en
Publisher:
Release Date : 1990
Adaptive Streamline Diffusion Finite Element Methods For Convection Diffusion Problems written by Kenneth Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Moving Mesh Finite Element Method For Time Dependent Convection Diffusion Problems
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Author : Matthew Maxwell McCoy
language : en
Publisher:
Release Date : 2021
Moving Mesh Finite Element Method For Time Dependent Convection Diffusion Problems written by Matthew Maxwell McCoy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic dissertations categories.
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.
Stabilized Finite Element Methods For Time Dependent Convection Diffusion Equations
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Author : Onur Baysal
language : en
Publisher:
Release Date : 2012
Stabilized Finite Element Methods For Time Dependent Convection Diffusion Equations written by Onur Baysal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Finite element method categories.
In this thesis, enriched finite element methods are presented for both steady and unsteady convection diffusion equations. For the unsteady case, we follow the method of lines approach that consists of first discretizing in space and then use some time integrator to solve the resulting system of ordinary differential equation. Discretization in time is performed by the generalized Euler finite difference scheme, while for the space discretization the streamline upwind Petrov-Galerkin (SUPG), the Residual free bubble (RFB), the more recent multiscale (MS) and specific combination of RFB with MS (MIX) methods are considered. To apply the RFB and the MS methods, the steady local problem, which is as complicated as the original steady equation, should be solved in each element. That requirement makes these methods quite expensive especially for two dimensional problems. In order to overcome that drawback the pseudo approximation techniques, which employ only a few nodes in each element, are used. Next, for the unsteady problem a proper adaptation recipe, including these approximations combined with the generalized Euler time discretization, is described. For piecewise linear finite element discretization on triangular grid, the SUPG method is used. Then we derive an efficient stability parameter by examining the relation of the RFB and the SUPG methods. Stability and convergence analysis of the SUPG method applied to the unsteady problem is obtained by extending the Burman's analysis techniques for the pure convection problem. We also suggest a novel operator splitting strategy for the transport equations with nonlinear reaction term. As a result two subproblems are obtained. One of which we may apply using the SUPG stabilization while the other equation can be solved analytically. Lastly, numerical experiments are presented to illustrate the good performance of the method.
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems
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Author : Bernardo Cockburn
language : en
Publisher:
Release Date : 1997
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems written by Bernardo Cockburn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
In this paper, we study the Local Discontinuous Galerkin methods for non-linear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.
An Adaptive Finite Element Method For Convection Diffusion Problems
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Author : William Gerard Szymczak
language : en
Publisher:
Release Date : 1982
An Adaptive Finite Element Method For Convection Diffusion Problems written by William Gerard Szymczak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Approximation theory categories.
Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-Görg Roos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Numerical Methods For Singularly Perturbed Differential Equations written by Hans-Görg Roos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Least Squares Streamline Diffusion Finite Element Approximations To Singularly Perturbed Convection Diffusion Problems
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Author :
language : en
Publisher:
Release Date : 1999
Least Squares Streamline Diffusion Finite Element Approximations To Singularly Perturbed Convection Diffusion Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
In this paper we introduce and study a least-squares finite element approximation for singularly perturbed convection-diffusion equations of second order. By introducing the flux (diffusive plus convective) as a new unknown, the problem is written in a mixed form as a first order system. Further, the flux is augmented by adding the lower order terms with a small parameter. The new first order system is approximated by the least-squares finite element method using the minus one norm approach of Bramble, Lazarov, and Pasciak [2]. Further, we estimate the error of the method and discuss its implementation and the numerical solution of some test problems.
Acta Numerica 1995 Volume 4
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13
Acta Numerica 1995 Volume 4 written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-13 with Mathematics categories.
Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.