Order of convergence of second order schemes based on the minmod limiter Academic Article uri icon


  • Many second order accurate nonoscillatory schemes are based on the minmod limiter, e.g., the NessyahuTadmor scheme. It is well known that the L p L_p -error of monotone finite difference methods for the linear advection equation is of order 1 / 2 1/2 for initial data in W 1 ( L p ) W^1(L_p) , 1 p 1leq pleq infty . For second or higher order nonoscillatory schemes very little is known because they are nonlinear even for the simple advection equation. In this paper, in the case of a linear advection equation with monotone initial data, it is shown that the order of the L 2 L_2 -error for a class of second order schemes based on the minmod limiter is of order at least 5 / 8 5/8 in contrast to the 1 / 2 1/2 order for any formally first order scheme.

published proceedings


author list (cited authors)

  • Popov, B., & Trifonov, O.

citation count

  • 9

complete list of authors

  • Popov, Bojan||Trifonov, Ognian

publication date

  • October 2006