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AuthorCockburn, Bernardo. author
TitleAdvanced Numerical Approximation of Nonlinear Hyperbolic Equations [electronic resource] : Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997 / by Bernardo Cockburn, Chi-Wang Shu, Claes Johnson, Eitan Tadmor ; edited by Alfio Quarteroni
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1998
Connect tohttp://dx.doi.org/10.1007/BFb0096351
Descript VI, 454 p. online resource

SUMMARY

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis


CONTENT

Approximate solutions of nonlinear conservation laws -- An introduction to the Discontinuous Galerkin method for convection-dominated problems -- Adaptive finite element methods for conservation laws -- Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws


Mathematics Partial differential equations Numerical analysis Thermodynamics Computational intelligence Mathematics Partial Differential Equations Numerical Analysis Thermodynamics Computational Intelligence



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