Liu, J-G; Wang, W-C, *Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows*,
SIAM Journal on Numerical Analysis, vol. 44 no. 6
(2006),
pp. 2456-2480 [doi] .
**Abstract:**

*We give an error estimate for the energy and helicity preserving scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ingredient in our a priori estimate is the permutation identities associated with the Jacobians, which are also a unique feature that distinguishes EHPS from standard finite difference schemes. © 2006 Society for Industrial and Applied Mathematics.*