A Local Discontinuous Galerkin Method Based on Variational Structure
Author | : |
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Total Pages | : 20 |
Release | : 2014 |
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Publisher | : |
Total Pages | : 20 |
Release | : 2014 |
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Author | : Shoaib Ahmad Goraya |
Publisher | : |
Total Pages | : |
Release | : 2019 |
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Author | : Bernardo Cockburn |
Publisher | : Springer Science & Business Media |
Total Pages | : 468 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642597211 |
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 | : Vít Dolejší |
Publisher | : Springer |
Total Pages | : 575 |
Release | : 2015-07-17 |
Genre | : Mathematics |
ISBN | : 3319192671 |
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 | : G. Duvant |
Publisher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642661653 |
1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t>o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o => au(x,t)/an=O, XEr, (2) u(x,t)=o => au(x,t)/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)/an = 0, respectively. These regions are not prescribed; thus we deal with a "free boundary" problem.
Author | : Hans Petter Langtangen |
Publisher | : Springer Nature |
Total Pages | : 395 |
Release | : 2019-09-26 |
Genre | : Mathematics |
ISBN | : 3030237885 |
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Author | : Francis X. Giraldo |
Publisher | : Springer Nature |
Total Pages | : 559 |
Release | : 2020-10-30 |
Genre | : Mathematics |
ISBN | : 3030550699 |
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 | : Beatrice Riviere |
Publisher | : SIAM |
Total Pages | : 202 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 0898717442 |
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 | : Morton E. Gurtin |
Publisher | : Springer Science & Business Media |
Total Pages | : 248 |
Release | : 2008-01-20 |
Genre | : Science |
ISBN | : 0387226567 |
Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.
Author | : Anders Logg |
Publisher | : Springer Science & Business Media |
Total Pages | : 723 |
Release | : 2012-02-24 |
Genre | : Computers |
ISBN | : 3642230997 |
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.