Titlebook: Numerical Solutions of Partial Differential Equations; Silvia Bertoluzza,Giovanni Russo,Chi-Wang Shu Textbook 2009 Birkh?user Basel 2009 d

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IntroductionThe purpose of these lecture notes is to provide an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws.

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Nonlinear Reconstruction and High-Order Schemes. In a finite-volume scheme, the basic unknown is the cell average ..

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Time DiscretizationIn these lecture notes, we will concentrate on the method of lines DG methods, that is, we do not discretize the time variable. Therefore, we will briefly discuss the issue of time discretization at the beginning.

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Discontinuous Galerkin Method for Conservation LawsThe discontinuous Galerkin method was first designed as an effective numerical method for solving hyperbolic conservation laws, which may have discontinuous solutions. In this section we will discuss the algorithm formulation, stability analysis, and error estimates for the discontinuous Galerkin method solving hyperbolic conservation laws.

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Silvia Bertoluzza,Giovanni Russo,Chi-Wang ShuThe review on central schemes, on error estimates for discontinuous Galerkin methods and on the use of wavelets in scientific computing form an excellent teaching material for graduate students.Includ

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https://doi.org/10.1007/978-3-7643-8940-6differential equation; numerical analysis; partial differential equation; scientific computing; wavelet;

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