Convergence of Spectral Methods for Nonlinear Conservation Laws | Zendy

Eitan Tadmor | Zendy

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Convergence of Spectral Methods for Nonlinear Conservation Laws

Author(s) -

Eitan Tadmor

Publication year - 1989

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/0726003

Subject(s) - conservation law , inviscid flow , mathematics , burgers' equation , nonlinear system , compact space , convergence (economics) , classification of discontinuities , mathematical analysis , fourier transform , scalar (mathematics) , classical mechanics , partial differential equation , physics , geometry , quantum mechanics , economics , economic growth

. We discuss the convergence of Fourier method for scalar nonlinear conservation laws which exhibitspontaneous shock discontinuities. Numerical tests indicate that the convergence may (and in fact in some cases weprove it must) fail, with or without post-processing of the numerical solution. Instead, we introduce here a new kind ofspectrally accurate vanishing viscosity to augment the Fourier approximation of such nonlinear conservation laws. Usingcompensated compactness arguments augmented ...

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