Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations

Author : Beatrice Riviere
Publisher : SIAM
Page : 202 pages
File Size : 43,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898717440

Get Book

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

Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and computation as it focuses on three primal DG methods?the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric interior penalty Galerkin?which are variations of interior penalty methods. The author provides the basic tools for analysis and discusses coding issues, including data structure, construction of local matrices, and assembling of the global matrix. Computational examples and applications to important engineering problems are also included.

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 55,9 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 : V. Thomee
Publisher : Springer
Page : 243 pages
File Size : 51,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387930

Get Book

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

Author : Vidar Thomee
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 49,9 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783540331223

Get Book

Galerkin Finite Element Methods for Parabolic Problems by Vidar Thomee Pdf

This book provides insight into the mathematics of Galerkin finite element method as applied to parabolic equations. The revised second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.

Author : Murat Uzunca
Publisher : Birkhäuser
Page : 105 pages
File Size : 55,5 Mb
Release : 2016-05-17
Category : Mathematics
ISBN : 9783319301303

Get Book

Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows by Murat Uzunca Pdf

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.

Author : Peter Knabner,Lutz Angerman
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 42,5 Mb
Release : 2006-05-26
Category : Mathematics
ISBN : 9780387217628

Get Book

Numerical Methods for Elliptic and Parabolic Partial Differential Equations by Peter Knabner,Lutz Angerman Pdf

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Author : Vít Dolejší,Miloslav Feistauer
Publisher : Springer
Page : 572 pages
File Size : 53,6 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 : Daniele Antonio Di Pietro,Alexandre Ern
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 47,5 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 : 52,5 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 : Abdul A. Khan,Wencong Lai
Publisher : CRC Press
Page : 218 pages
File Size : 51,5 Mb
Release : 2014-03-03
Category : Science
ISBN : 9781482226010

Get Book

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

Replacing the Traditional Physical Model Approach Computational 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 laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.

Author : Thomas Carraro,Michael Geiger,Stefan Körkel,Rolf Rannacher
Publisher : Springer
Page : 422 pages
File Size : 47,9 Mb
Release : 2015-10-26
Category : Mathematics
ISBN : 9783319233215

Get Book

Multiple Shooting and Time Domain Decomposition Methods by Thomas Carraro,Michael Geiger,Stefan Körkel,Rolf Rannacher Pdf

This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.

Author : Koen Hillewaert
Publisher : Presses univ. de Louvain
Page : 173 pages
File Size : 53,5 Mb
Release : 2013-02-10
Category : Science
ISBN : 9782875581198

Get Book

Development of the Discontinuous Galerkin Method for High-resolution, Large Scale CFD and Acoustics in Industrial Geometries by Koen Hillewaert Pdf

The main objective of this work is the practical development of the discontinuous Galerkin method, arguably the most mature high-order discretisation, for the scale resolving simulations of turbomachinery flows.

Author : Marco L. Bittencourt,Ney A. Dumont,Jan S. Hesthaven
Publisher : Springer
Page : 700 pages
File Size : 48,5 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783319658704

Get Book

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 by Marco L. Bittencourt,Ney A. Dumont,Jan S. Hesthaven Pdf

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Author : Peter Knabner,Lutz Angermann
Publisher : Springer Nature
Page : 811 pages
File Size : 50,6 Mb
Release : 2021-11-19
Category : Mathematics
ISBN : 9783030793852

Get Book

Numerical Methods for Elliptic and Parabolic Partial Differential Equations by Peter Knabner,Lutz Angermann Pdf

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Author : Leonid Sokolinsky,Mikhail Zymbler
Publisher : Springer Nature
Page : 327 pages
File Size : 40,6 Mb
Release : 2021-07-08
Category : Computers
ISBN : 9783030816919

Get Book

Parallel Computational Technologies by Leonid Sokolinsky,Mikhail Zymbler Pdf

This book constitutes refereed proceedings of the 15th International Conference on Parallel Computational Technologies, PCT 2021, held in March-April 2021. Due to the COVID-19 pandemic the conference was held online. The 22 revised full papers presented were carefully reviewed and selected from 89 submissions. The papers are organized in topical sections on high performance architectures, tools and technologies; parallel numerical algorithms; supercomputer simulation.