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

  • Authors
  • Bernardo Cockburn
  • Chi-Wang Shu
  • Claes Johnson
  • Eitan Tadmor
  • Editors
  • Alfio Quarteroni

Part of the Lecture Notes in Mathematics book series (LNM, volume 1697)

About this book

Introduction

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.

Keywords

differential equation finite element method hyperbolic equation nonlinear partial differential equation partial differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0096351
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-64977-9
  • Online ISBN 978-3-540-49804-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book