Jan S. Hesthaven's Books

Nodal Discontinuous Galerkin Methods

Algorithms, Analysis, and Applications

By: Jan S. Hesthaven,Tim Warburton

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Nodal Discontinuous Galerkin Methods

Algorithms, Analysis, and Applications

By: Jan S. Hesthaven,Tim Warburton

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.

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Page Count

507

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387720650

ISBN 13

9780387720654

Numerical Methods for Conservation Laws

From Analysis to Algorithms

By: Jan S. Hesthaven

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Numerical Methods for Conservation Laws

From Analysis to Algorithms

By: Jan S. Hesthaven

Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.

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Page Count

571

Publisher

SIAM

Published Date

ISBN 10

1611975093

ISBN 13

9781611975093

Spectral Methods for Time-Dependent Problems

By: Jan S. Hesthaven,Sigal Gottlieb,David Gottlieb

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Spectral Methods for Time-Dependent Problems

By: Jan S. Hesthaven,Sigal Gottlieb,David Gottlieb

Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.

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Publisher

Cambridge University Press

Published Date

ISBN 10

113945952X

ISBN 13

9781139459525

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

By: Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations

By: Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

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Page Count

139

Publisher

Springer

Published Date

ISBN 10

3319224700

ISBN 13

9783319224701

Book's by Jan S. Hesthaven

Nodal Discontinuous Galerkin Methods

Nodal Discontinuous Galerkin Methods

Numerical Methods for Conservation Laws

Numerical Methods for Conservation Laws

Spectral Methods for Time-Dependent Problems

Spectral Methods for Time-Dependent Problems

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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