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Titlebook: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012; Selected papers from Mejdi Azaïez,Henda El Fekih,Jan S.

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978-3-319-37858-9Springer International Publishing Switzerland 2014
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The Geometric Basis of Numerical Methods,The relation between physics, its description in terms of partial differential equations and geometry is explored in this paper. Geometry determines the correct weak formulation in finite element methods and also dictates which basis functions should be employed to obtain discrete well-posedness.
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Mejdi Azaïez,Henda El Fekih,Jan S. HesthavenIncludes supplementary material:
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High-Order ADI Schemes for Convection-Diffusion Equations with Mixed Derivative Terms,ffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer (Appl Numer Math 42:213–233, 2002). Different numerical discretizations which lead to schemes which are fourth-order accurate in space and second-order accurate in time are discussed.
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Lecture Notes in Computational Science and Engineeringhttp://image.papertrans.cn/s/image/873897.jpg
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https://doi.org/10.1007/978-3-319-01601-6High-order methods; Partial differential equations; Spectral methods
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Karsten Bock,Jörg Stillerluster of workstations. An alternative parallelisation of the algorithm using MPI is also discussed. Experimental results show that a significant reduction of computing time is possible, achieving approximately a linear speed-up with the number of parallel processors used.
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