Discontinuous Galerkin methods Lecture 1 - Brown University

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Start by saying thanks! • To the main organizers • D. Stanescu and A. Porter (UWY) • Funding agencies to enable the work • NSF, ARO, DARPA, AFOSR, Sloan Foundation • Collaborators over time • Tim Warburton • David Gottlieb • -- and many others
A brief overview of what’s to come • Lecture 1: Introduction, Motivation, History • Lecture 2: Basic elements of DG-FEM • Lecture 3: Linear systems and some theory • Lecture 4: A bit more theory and discrete stability • Lecture 5: Attention to implementations • Lecture 6: Nonlinear problems and properties • Lecture 7: Problems with discontinuities and shocks • Lecture 8: Higher order/Global problems
Page 1: RMMC 2008 Discontinuous Galerkin me
Page 5 and 6: Lecture 1 • Why do we need someth
Page 7 and 8: What is causing this growing gap ?
Page 9 and 10: Can we close the gap ? It is the al
Page 11 and 12: Why high-order accuracy ? We may be
Page 13 and 14: U(x, 1.5 Why high-order accuracy ?
Page 15 and 16: We arrive at a more straightforward
Page 17 and 18: to advance the equations in time, t
Page 19 and 20: Finite difference schemes • Main
Page 21 and 22: evaluation of these fluxes is not s
Page 23 and 24: has to vanish for all φh ∈ Vh, t
Page 25 and 26: D So lets see how we can achieve th
Page 27 and 28: sic understanding of the schemes th
Page 29 and 30: allow one to recover a meaningful g
Page 31 and 32: 1 Introduction The basics of DG-FEM
Page 33 and 34: ount of history A brief history ale
Page 35 and 36: A brief history • The last decade
Page 37: A brief overview - and what now ?

Discontinuous Galerkin methods Lecture 1 - Brown University

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