Publications [#322467] of J. Thomas Beale
- Beale, JT; Majda, A, Vortex methods. ii: Higher order accuracy in two and three dimensions,
Mathematics of Computation, vol. 39 no. 159
pp. 29-52, American Mathematical Society (AMS) [doi]
(last updated on 2019/11/20)
In an earlier paper the authors introduced a new version of the vortex method for three-dimensional, incompressible flows and proved that it converges to arbitrarily high order accuracy, provided we assume the consistency of a discrete approximation to the Biot-Savart Law. We prove this consistency statement here, and also derive substantially sharper results for two-dimensional flows. A complete, simplified proof of convergence in two dimensions is included. © 1982 American Mathematical Society.