Discontinuous Galerkin methods Lecture 1 - Brown University

More documents

Recommendations

Info

A brief history • Extension from scalar conservation laws in late 1980’s to system in late 1990’s (Cockburn/Shu) • Development of limiters and RKDG • Nodes, modes and large codes (H, Warburton, Karniadakis etc etc - from 1995) • Maxwell’s equations, MHD, water waves, elasticity etc -- last decade has seen explosion • Higher order problems - IP (Arnold, 1982), BR (Bassi/Rebay, 1997), LDG (Cockburn/Shu1998)
A brief history • The last decade has seen an explosion in activities • Hamilton-Jacobi equations • Non-coercive problems and spectral accuracy • Adaptive solution techniques • Improved solvers • Advanced time-integration <strong>methods</strong> • Large scale production codes • etc, etc
Page 1 and 2: RMMC 2008 Discontinuous Galerkin me
Page 3 and 4: A brief overview of what’s to com
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: ount of history A brief history ale
Page 37: A brief overview - and what now ?

Discontinuous Galerkin methods Lecture 1 - Brown University

Create successful ePaper yourself

Delete template?

Save as template?