Total variation and error estimates for spectral viscosity approximations

Journal Article · Fri Jan 01 04:00:00 EST 1993 · Mathematics of Computation; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1993-1153170-9· OSTI ID:6647458

Tadmor, E

We study the behavior of spectral viscosity approximations to nonlinear 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[sup 1]-stable and hence total-variation bounded. Moreover, the spectral viscosity solutions are shown to be Lip[sup +]-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. 16 refs.

• OSTI ID: 6647458
• Journal Information: Mathematics of Computation; (United States), Journal Name: Mathematics of Computation; (United States) Vol. 60:201; ISSN 0025-5718; ISSN MCMPAF
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
CONVERGENCE
DIFFERENTIAL EQUATIONS
ENTROPY
EQUATIONS
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SCALARS
THERMODYNAMIC PROPERTIES
TRANSFORMATIONS
VISCOSITY