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Titlebook: Numerical Models for Differential Problems; Alfio Quarteroni Textbook 20142nd edition Springer International Publishing 2014 PDE.analysis.

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书目名称Numerical Models for Differential Problems
编辑Alfio Quarteroni
视频video
概述Author faces here the basic concepts for the numerical modeling of partial differential equations.An outstanding reference work in this branch of applied mathematics.In particular, the author discuss
丛书名称MS&A
图书封面Titlebook: Numerical Models for Differential Problems;  Alfio Quarteroni Textbook 20142nd edition Springer International Publishing 2014 PDE.analysis.
描述In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
出版日期Textbook 20142nd edition
关键词PDE; analysis; numerical modelling
版次2
doihttps://doi.org/10.1007/978-88-470-5522-3
isbn_softcover978-88-470-5883-5
isbn_ebook978-88-470-5522-3Series ISSN 2037-5255 Series E-ISSN 2037-5263
issn_series 2037-5255
copyrightSpringer International Publishing 2014
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Discontinuous element methods (DG and mortar),ectral element method (.). This chapter deals with approximation techniques based on subspaces of polynomials that are discontinuous between elements. We will, in particular, introduce the so-called . method (DG) and the . method. We will carry out this for the Poisson problem first, and then genera
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Nonlinear hyperbolic problems,otably their ability to generate discontinuous solutions also in the case of continuous initial and boundary data. The numerical approximation of these problems is far from easy. Here we will simply limit ourselves to point out how finite difference and finite element schemes can be applied in the c
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Navier-Stokes equations,id’s velocity, . the pressure divided by the density (which will simply be called “pressure”), . the kinematic viscosity, . the dynamic viscosity, and . a forcing term per unit of mass that we suppose belongs in L.(ℝ.; [L.(Ω)].) (see .). The first equation is that of conservation of linear momentum,
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Optimal control of partial differential equations,assical theory in functional spaces “à la J.L.Lions”, see [., .]; then we will address the methodology based on the use of the Lagrangian functional (see, e.g., [., ., .]). Finally, we will show two different numerical approaches for control problems, based on the Galerkin finite element method.
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