Bertoluzza S., Falletta S., Russo G., Shu C.-W. Numerical Solutions of Partial Differential Equations

Germany: Springer, Centre de Recerca Matemàtica (CRM), 2009. — 208 p. — (Advanced Courses in Mathematics CRM Barcelona). — ISBN: 978-3-7643-8939-0.This book contains an expanded and smoothed version of lecture notes delivered by the authors at the Advanced School on Numerical Solutions of Partial Di - ential Equations.Wavelets and Partial Differential EquationsWhatisaWavelet?
The Fundamental Property of Wavelets
Wavelets for Partial Differential Equations
High Order Shock-Capturing Schemes for Balance Laws Giovanni RussoUpwind Scheme for Systems
The Numerical Flux Function
Nonlinear Reconstruction and High-Order Schemes
Central Schemes
Systems with Stiff Source
Appendix: Butcher Tableau of IMEX-RK
Discontinuous Galerkin Methods: General Approach and StabilityTime Discretization
Discontinuous Galerkin Method for Conservation Laws
Discontinuous Galerkin Method for Convection-Diffusion Equations
Discontinuous Galerkin Method for PDEs Containing Higher-Order Spatial Derivatives