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A multilevel characteristics method for periodic convection‐dominated diffusion problems
Author(s) -
Marion M.,
Mollard A.
Publication year - 2000
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(200001)16:1<107::aid-num8>3.0.co;2-0
Subject(s) - discretization , mathematics , interpolation (computer graphics) , stability (learning theory) , convection–diffusion equation , discretization of continuous features , partial differential equation , diffusion , temporal discretization , term (time) , mathematical analysis , discretization error , computer science , animation , physics , computer graphics (images) , quantum mechanics , machine learning , thermodynamics
In this article we introduce a multilevel method in space and time for the approximation of a convection‐diffusion equation. The spatial discretization is of pseudo‐spectral Fourier type, while the time discretization relies on the characteristics method. The approximate solution is obtained as the sum of two components that are advanced in time using different time‐steps. In particular, this requires the introduction of two sets of discretized characteristics curves and of two interpolation operators. We investigate the stability of the scheme and derive some error estimates. They indicate that the high‐frequency term can be integrated with a larger time‐step. Numerical experiments illustrate the gain in computing time due to the multilevel strategy. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 107–132, 2000