Discontinuous Galerkin methods Lecture 3 - Brown University

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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
Lecture 3 • Let’s briefly recall what we know • Constructing fluxes for linear systems • The local basis and Legendre polynomials • Approximation theory on the interval
Page 1: RMMC 2008 Discontinuous Galerkin me
Page 5 and 6: Let us recall We already know a lot
Page 7 and 8: ∂t ∂x ∂y assume approximation
Page 9 and 10: d dt b u dx = d (λt − a)u −
Page 11 and 12: which one can attempt to express us
Page 13 and 14: x ∈ D Lets move on At this point
Page 15 and 16: mial basis). This leaves only the q
Page 17 and 18: erty quadrature ˜Pn(r) of wesuch u
Page 19 and 20: It suggests that it is reasonable t
Page 21 and 22: Local approximation - an example De
Page 23 and 24: e notation A second look at approxi
Page 25 and 26: simplicity, we assume that all elem
Page 27 and 28: (N +1+σ)! n=N+1 v − vh Approxima
Page 29 and 30: h h This implies vh(r) = ˜vh(r)+
Page 31 and 32: the situation is different. Note th
Page 33: Lets summarize Fluxes: • For line

Discontinuous Galerkin methods Lecture 3 - Brown University

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