Advanced numerical approximation of nonlinear hyperbolic equations
Subtitle: 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: B. Cockburn ... [et al.] ; editor, Alfio Quarteroni.
Contributors: Cockburn, B.; Quarteroni, Alfio.; Centro internazionale matematico estivo.
Series: Lecture notes in mathematics,; 1697; Lecture notes in mathematics (Springer-Verlag) ;; 1697.
Publisher: Springer
Published: 1998
Place of publication: Berlin; New York
Language: eng
Number of pages: 450
Subjects: Differential equations, Hyperbolic -- Numerical solutions -- Congresses; Differential equations, Nonlinear -- Numerical solutions -- Congresses
Description: 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.
Notes: Includes bibliographical references.