The weighted particle method for convection-diffusion equations. II. The anisotropic case
P. Degond and S. Mas-Gallic
Math. Comp. 53 (1989), 509-525
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Abstract: This paper is devoted to the presentation and the analysis of a new particle method for convection-diffusion equations. The method has been presented in detail in the first part of this paper for an isotropic diffusion operator. This part is concerned with the extension of the method to anisotropic diffusion operators. The consistency and the accuracy of the method require much more complex conditions on the cutoff functions than in the isotropic case. After detailing these conditions, we give several examples of cutoff functions which can be used for practical computations. A detailed error analysis is then performed.
Degond and S.
Mas-Gallic, The weighted particle method for
convection-diffusion equations. I. The case of an isotropic
viscosity, Math. Comp. 53
(1989), no. 188, 485–507. MR 983559
Mas-Gallic and P.-A.
Raviart, A particle method for first-order symmetric systems,
Numer. Math. 51 (1987), no. 3, 323–352. MR 895090
D. C. Montgomery & D. A. Tidman, Plasma Kinetic Theory, McGraw-Hill, New York, 1964.
- P. Degond & S. Mas-Gallic, "The weighted particle method for convection-diffusion equations, Part 1: The isotropic case," Math. Comp., v. 53, 1989, pp. 485-507. MR 983559 (90g:65126)
- S. Mas-Gallic & P. A. Raviart, "A particle method for first-order symmetric systems," Numer. Math., v. 51, 1987, pp. 323-352. MR 895090 (88d:65132)
- D. C. Montgomery & D. A. Tidman, Plasma Kinetic Theory, McGraw-Hill, New York, 1964.
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