The weighted particle method for convection-diffusion equations. II. The anisotropic case

Degond, P.; Mas-Gallic, S.

doi:10.1090/S0025-5718-1989-0983560-5

The weighted particle method for convection-diffusion equations. II. The anisotropic case
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by P. Degond and S. Mas-Gallic PDF

Math. Comp. 53 (1989), 509-525 Request permission

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.

References

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, DOI 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, DOI 10.1007/BF01400118

Plasma Kinetic Theory