Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23-28, 1997
1998
ISBN: 978-3-540-64977-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1697, 454 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1410 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Cockburn, B.

Johnson, C.

Tadmor, E.

Shu, C. -W.

Quarteroni, Alfio

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Thermodynamik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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.