The weighted particle method for convection-diffusion equations. II. The anisotropic case
Authors: P. Degond and S. Mas-Gallic
Journal: Math. Comp. 53 (1989), 509-525
MSC: Primary 65M99
MathSciNet review: 983560
Full-text PDF Free Access
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.
-  P. 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, https://doi.org/10.1090/S0025-5718-1989-0983559-9
-  S. Mas-Gallic and P.-A. Raviart, A particle method for first-order symmetric systems, Numer. Math. 51 (1987), no. 3, 323–352. MR 895090, https://doi.org/10.1007/BF01400118
-  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.
Retrieve articles in Mathematics of Computation with MSC: 65M99
Retrieve articles in all journals with MSC: 65M99