$L^1$–framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations
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- by Gui-Qiang Chen and Kenneth H. Karlsen PDF
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Abstract:
We develop a general $L^1$–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach. We apply our $L^1$–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without imposition of bounded variation of the approximate solutions. Finally, as an example of a direct application of this framework to numerical methods, we focus on a linear convection-diffusion model equation and derive an $L^1$ error estimate for an upwind-central finite difference scheme.References
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Additional Information
- Gui-Qiang Chen
- Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
- MR Author ID: 249262
- ORCID: 0000-0001-5146-3839
- Email: gqchen@math.northwestern.edu
- Kenneth H. Karlsen
- Affiliation: Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway
- Email: kennethk@math.uio.no
- Received by editor(s): January 11, 2004
- Published electronically: December 28, 2004
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 937-963
- MSC (2000): Primary 35K65, 35B35, 35G25, 35D99
- DOI: https://doi.org/10.1090/S0002-9947-04-03689-X
- MathSciNet review: 2187640