Discontinuous Galerkin Methods

Author : Vít Dolejší,Miloslav Feistauer
Publisher : Springer
Page : 572 pages
File Size : 46,7 Mb
Release : 2015-07-17
Category : Mathematics
ISBN : 9783319192673

Get Book

Discontinuous Galerkin Method by Vít Dolejší,Miloslav Feistauer Pdf

The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

Author : Jan S. Hesthaven,Tim Warburton
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 52,8 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 9780387720654

Get Book

Nodal Discontinuous Galerkin Methods by Jan S. Hesthaven,Tim Warburton Pdf

This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642597213

Get Book

Discontinuous Galerkin Methods by Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu Pdf

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 : Daniele Antonio Di Pietro,Alexandre Ern
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 40,8 Mb
Release : 2011-11-03
Category : Mathematics
ISBN : 9783642229800

Get Book

Mathematical Aspects of Discontinuous Galerkin Methods by Daniele Antonio Di Pietro,Alexandre Ern Pdf

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.

Author : Andrea Cangiani,Zhaonan Dong,Emmanuil H. Georgoulis,Paul Houston
Publisher : Springer
Page : 131 pages
File Size : 43,7 Mb
Release : 2017-11-27
Category : Mathematics
ISBN : 9783319676739

Get Book

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes by Andrea Cangiani,Zhaonan Dong,Emmanuil H. Georgoulis,Paul Houston Pdf

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.

Author : Beatrice Riviere
Publisher : SIAM
Page : 201 pages
File Size : 51,7 Mb
Release : 2008-12-18
Category : Mathematics
ISBN : 9780898716566

Get Book

Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations by Beatrice Riviere Pdf

Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.

Author : Gary Cohen,Sébastien Pernet
Publisher : Springer
Page : 381 pages
File Size : 45,5 Mb
Release : 2016-08-05
Category : Technology & Engineering
ISBN : 9789401777612

Get Book

Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations by Gary Cohen,Sébastien Pernet Pdf

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.

Author : Abdul A. Khan,Wencong Lai
Publisher : CRC Press
Page : 208 pages
File Size : 51,5 Mb
Release : 2014-03-03
Category : Science
ISBN : 9781482226027

Get Book

Modeling Shallow Water Flows Using the Discontinuous Galerkin Method by Abdul A. Khan,Wencong Lai Pdf

Replacing the Traditional Physical Model ApproachComputational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation l

Author : Xiaobing Feng,Ohannes Karakashian,Yulong Xing
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 51,5 Mb
Release : 2013-11-08
Category : Mathematics
ISBN : 9783319018188

Get Book

Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations by Xiaobing Feng,Ohannes Karakashian,Yulong Xing Pdf

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 : V. Thomee
Publisher : Springer
Page : 243 pages
File Size : 43,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387930

Get Book

Galerkin Finite Element Methods for Parabolic Problems by V. Thomee Pdf

Author : Z. J. Wang
Publisher : World Scientific
Page : 471 pages
File Size : 48,7 Mb
Release : 2011
Category : Science
ISBN : 9789814313186

Get Book

Adaptive High-order Methods in Computational Fluid Dynamics by Z. J. Wang Pdf

This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

Author : Francis X. Giraldo
Publisher : Springer
Page : 559 pages
File Size : 43,5 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 3030550710

Get Book

An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases by Francis X. Giraldo Pdf

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.

Author : Timothy J. Barth,Herman Deconinck
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662038826

Get Book

High-Order Methods for Computational Physics by Timothy J. Barth,Herman Deconinck Pdf

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 : Nguyen Trung Viet,Dou Xiping,Tran Thanh Tung
Publisher : Springer Nature
Page : 1483 pages
File Size : 52,5 Mb
Release : 2019-09-25
Category : Science
ISBN : 9789811502910

Get Book

APAC 2019 by Nguyen Trung Viet,Dou Xiping,Tran Thanh Tung Pdf

This book presents selected articles from the International Conference on Asian and Pacific Coasts (APAC 2019), an event intended to promote academic and technical exchange on coastal related studies, including coastal engineering and coastal environmental problems, among Asian and Pacific countries/regions. APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE). APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE).

Author : Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 696 pages
File Size : 50,7 Mb
Release : 2003
Category : Mathematics
ISBN : 3540440518

Get Book

Geometric Analysis and Nonlinear Partial Differential Equations by Stefan Hildebrandt Pdf

This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.