Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

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Springer Science & Business Media, Dec 18, 2007 - Mathematics - 502 pages
Mathematicsisplayinganevermoreimportantroleinthephysicalandbiol- ical sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and tea- ing, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose ofthistextbookseriesistomeetthecurrentandfutureneedsoftheseadvances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface The algorithms, methods, and Matlab implementations described in this text have been developed during almost a decade of collaboration. During this time we have worked to simplify the basic methods and make the ideas more accessible to a broad audience. Many people, both students and colleagues, have helped during the development of this project and we are grateful for all their suggestions and input.
 

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Contents

ntroduction
1
A brief account of history
11
Scope of text and audience
17
aking it work in one dimension 43
42
Elementwise operations
51
Getting the grid together and computing the metric
57
Dealing with time
63
Exercises
72
Error estimates for nonlinear problems with smooth solutions
135
Jeyond one dimension
169
ligherorder equations 243
242
The compressible NavierStokes equations
314
pectral properties of discontinuous Galerkin operators
331
The Maxwell eigenvalue problem
343
Curvilinear elements and nonconforming discretizations
373
nto the third dimension
407

Stability
83
Nonlinear problems
115
Aliasing instabilities and filter stabilization
123
Jacobi polynomials and beyond
445
Software variables and helpful scripts 461
460
Copyright

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Page 481 - Construction of curvilinear co-ordinate systems and application to mesh generation'.
Page 491 - G. STRANG and GJ Fix, Analysis of the Finite Element Method, Prentice-Hall, 1973.

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