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A particle method for first-order symmetric systems. (English) Zbl 0625.65084

Convergence and stability theorems are proved for a particle method for symmetric, hyperbolic systems. The algorithm relies on a well-chosen smoothing procedure to capture information travelling at speeds different from the particle velocities. The proof of convergence is based on the stability result and on a lemma from approximation theory.
Reviewer: G.Hedstrom

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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References:

[1] Anderson, C., Greengard, C.: On vortex methods. SIAM J. Numer. Anat.22, 413-440 (1985) · Zbl 0578.65121
[2] Beale, J.T.: A convergent 3-D vortex method with greed-free stretching. (preprint) · Zbl 0602.76024
[3] Beale, J.T., Majda, A.: Vortex methods I: Convergence in three dimensions. Math. Comput.32, 1-27 (1982) · Zbl 0488.76024
[4] Beale, J.T., Majda, A.: Vortex methods II: Higher order accuracy in two and three dimensions. Math. Comput.32, 29-52 (1982) · Zbl 0488.76025
[5] Birdsall, C.K., Langdon, A.B.: Plasma Physics via Computer Simulation. New-York: Mc Grew-Hill 1985
[6] Cottet, G.H.: Méthodes particulaires pour l’équation d’Euler dans le plan, Thèse de 3{\(\deg\)} cycle, Université P. et M. Curié, Paris 1982
[7] Cottet, G.H.: Convergence of a vortex-in-cell method for the two-dimensional Euler equations. Math. Comput. (to appear) · Zbl 0652.65068
[8] Cottet, G.H.: On the convergence of vortex methods in two and three dimensions (preprint)
[9] Cottet, G.H., Raviart, P.-A.: Particle methods for the one-dimensional Vlasov-Poisson equation. SIAM J. Numer. Anal.21, 52-76 (1984) · Zbl 0549.65084
[10] Cottet, G.H., Raviart, P.-A.: On particle-in-cell methods for the Vlasov-Poisson equations. Trans. Theory Stat. Phys. (to appear) · Zbl 0549.65084
[11] Duderstadt, J.J., Martin, M.-R.: Transport Theory. New York: John Wiley 1979 · Zbl 0407.76001
[12] Gingold, R.A., Monaghan, J.-J.: Shock simulation by the particle method S.P.H. J. Comput. Phys.52, 374-389 (1983) · Zbl 0572.76059
[13] Hald, O.: Convergence of vortex methods II. SIAM J. Numer. Anal.16, 726-755 (1979) · Zbl 0427.76024
[14] Harlow, F.: The particle-in-cell method for fluid dynamics. In: Methods in Computational Physics (B. Alder, S. Fernbach, M. Rotenberg, eds.), vol. 3. New York, Academic Press 1964 · Zbl 0158.44501
[15] Hockney, R.W., Eastwood, J.-W.: Computer Simulation using Particles. New York: Mc Graw-Hill 1981 · Zbl 0662.76002
[16] Leonard, A.: Vortex methods for flow simulations. J. Comput. Phys.37, 289-335 (1980) · Zbl 0438.76009
[17] Leonard, A.: Computing, Three-dimensional incompressible flows with vortex elements. Ann. Rev. Fluid Mech.17, 523-559 (1985) · Zbl 0596.76026
[18] Mas-Gallic, S., Raviart, P.-A.: Particle approximation of convection-diffusion problems. (to appear) · Zbl 0863.76095
[19] Raviart, P.-A.: An analysis of particle methods. In: Numerical Methods in Fluid Dynamics (F. Brezzi, ed.). Lecture Notes in Mathematics vol. 1127. Berlin, Springer 1985 · Zbl 0598.76003
[20] Raviart, P.-A.: Particle approximation of linear hyperbolic equations of the first order. In: Numerical Analysis Proceedings 1983 (D. Griffiths, ed.), pp. 142-158. Lecture Notes in Mathematics, vol. 1066. Berlin, Heidelberg, New York: Springer 1984
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