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Author: Jens Lang
Publisher:
ISBN:
Category :
Languages : de
Pages : 14
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Book Description
Author: Jens Lang
Publisher:
ISBN:
Category :
Languages : de
Pages : 14
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Book Description
Author: Pavel B. Bochev
Publisher: Springer Science & Business Media
ISBN: 0387689222
Category : Mathematics
Languages : en
Pages : 669
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Book Description
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
ISBN: 3642597211
Category : Mathematics
Languages : en
Pages : 468
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Book Description
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Author: Haihang You
Publisher:
ISBN:
Category :
Languages : en
Pages : 112
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Book Description
The Discontinuous Galerkin Method is one variant of the Finite Element Methods for solving partial differential equations, which was first introduced by Reed and Hill in 1970's [27]. Discontinuous Galerkin Method (DGFEM) differs from the standard Galerkin FEM that continuity constraints are not imposed on the inter-element boundaries. It results in a solution which is composed of totally piecewise discontinuous functions. The absence of continuity constraints on the inter-element boundaries implies that DG method has a great deal of flexibility at the cost of increasing the number of degrees of freedom. This flexibility is the source of many but not all of the advantages of the DGFEM method over the Continuous Galerkin (CGFEM) method that uses spaces of continuous piecewise polynomial functions and other "less standard" methods such as nonconforming methods. As DGFEM method leads to bigger system to solve, theoretical and practical approaches to speed it up are our main focus in this dissertation. This research aims at designing and building an adaptive discontinuous Galerkin finite element method to solve partial differential equations with fast time for desired accuracy on modern architecture.
Author: Xiaobing Feng
Publisher: Springer Science & Business Media
ISBN: 3319018183
Category : Mathematics
Languages : en
Pages : 289
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Book Description
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
Author: Michael Authur Saum
Publisher:
ISBN:
Category :
Languages : en
Pages : 221
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Book Description
A unified mathematical and computational framework for implementation of an adaptive discontinuous Galerkin (DG) finite element method (FEM) is developed using the symmetric interior penalty formulation to obtain numerical approximations to solutions of second and fourth order elliptic partial deferential equations. The DG-FEM formulation implemented allows for h-adaptivity and has the capability to work with linear, quadratic, cubic, and quartic polynomials on triangular elements in two dimensions. Two different formulations of DG are implemented based on how fluxes are represented on interior edges and comparisons are made. Explicit representations of two a posteriori error estimators, a residual based type and a "local" based type, are extended to include both Dirichlet and Neumann type boundary conditions on bounded domains. New list-based approaches to data management in an adaptive computational environment are introduced in an effort to utilize computational resources in an efficient and flexible manner.
Author: Wolfgang Bangerth
Publisher: Birkhäuser
ISBN: 303487605X
Category : Mathematics
Languages : en
Pages : 216
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Book Description
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.
Author: Zhangxin Chen
Publisher: Springer Science & Business Media
ISBN: 3540240780
Category : Science
Languages : en
Pages : 415
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Book Description
Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 366203882X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Author: Murat Uzunca
Publisher: Birkhäuser
ISBN: 3319301306
Category : Mathematics
Languages : en
Pages : 111
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Book Description
The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence.As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
