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 / Edition 1

by B. Cockburn, Alfio Quarteroni, C. Johnson, C.-W. Shu, E. Tadmor

Overview

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.

Product Details

ISBN-13:	9783540649779
Publisher:	Springer Berlin Heidelberg
Publication date:	12/04/1998
Series:	Lecture Notes in Mathematics , #1697
Edition description:	1998
Pages:	454
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

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.