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Lecture notes from the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications held in Bellaterra, November 15–22, 2007. Contents: Silvia Bertoluzza and Silvia Falletta, Wavelets and partial differential equations (1–57); Giovanni Russo, High-order shock-capturing schemes for balance laws (59–147); Chi-Wang Shu, Discontinuous Galerkin methods: general approach and stability (149–201)

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