Discontinuous Galerkin methods Lecture 3 - Brown University

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Let us recall We already know a lot about the basic DG-FEM • Stability is provided by carefully choosing the numerical flux. • Accuracy appear to be given by the local solution representation. • We can utilize major advances on monotone schemes to design fluxes. • The scheme generalizes with very few changes to very general problems -- multidimensional systems of conservation laws.
Let us recall We already know a lot about the basic DG-FEM • Stability is provided by carefully choosing the numerical flux. • Accuracy appear to be given by the local solution representation. • We can utilize major advances on monotone schemes to design fluxes. • The scheme generalizes with very few changes to very general problems -- multidimensional systems of conservation laws. At least in principle -- but what can we actually prove ?
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Page 3: Lecture 3 • Let’s briefly recal
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Page 9 and 10: d dt b u dx = d (λt − a)u −
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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
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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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