Summary
We present and study a conservative particle method of approximation of linear hyperbolic and parabolic systems. This method is based on an extensive use of cut-off functions. We prove its convergence inL 2 at the order\(\varepsilon ^2 + \frac{{h^m }}{{\varepsilon ^{m + 1} }}\) as soon as the cut-off function belongs toW m+1.1.
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Dedicated to Professor Joachim Nitsche on the occasion of his 60th birthday
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Mas-Gallic, S., Raviart, P.A. A particle method for first-order symmetric systems. Numer. Math. 51, 323–352 (1987). https://doi.org/10.1007/BF01400118
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DOI: https://doi.org/10.1007/BF01400118