Total variation and error estimates for spectral viscosity approximations
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- Math. Comp. 60 (1993), 245-256 Request permission
Abstract:
We study the behavior of spectral viscosity approximations to non-linear scalar conservation laws. We show how the spectral viscosity method compromises between the total-variation bounded viscosity approximations— which are restricted to first-order accuracy—and the spectrally accurate, yet unstable, Fourier method. In particular, we prove that the spectral viscosity method is ${L^1}$-stable and hence total-variation bounded. Moreover, the spectral viscosity solutions are shown to be ${\text {Lip}^ + }$-stable, in agreement with Oleinik’s E-entropy condition. This essentially nonoscillatory behavior of the spectral viscosity method implies convergence to the exact entropy solution, and we provide convergence rate estimates of both global and local types.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 60 (1993), 245-256
- MSC: Primary 35L65; Secondary 65M06, 65M12, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-1993-1153170-9
- MathSciNet review: 1153170