Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws | Zendy

Yvon Maday | Zendy; Sidi Mahmoud Kaber | Zendy; Eitan Tadmor | Zendy

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Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws

Author(s) -

Yvon Maday,

Sidi Mahmoud Kaber,

Eitan Tadmor

Publication year - 1993

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 - 10.1137/0730016

Subject(s) - mathematics , legendre polynomials , conservation law , nonlinear system , mathematical analysis , boundary value problem , legendre transformation , compact space , bounded function , pseudospectral optimal control , convergence (economics) , scalar (mathematics) , pseudo spectral method , geometry , physics , fourier transform , fourier analysis , quantum mechanics , economics , economic growth

. In this paper we study the Legendre Spectral Viscosity (SV) method for the approximate solution of initialboundaryvalue problems associated with nonlinear conservation laws. We prove that by adding a small amount of spectralviscosity, bounded solutions of the Legendre SV method converge to the exact scalar entropy solution. Our convergence proofis based on compensated compactness arguments, and therefore applies to certain 2 \Theta 2 systems. Finally, we present numericalexperiments for...

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