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

abstract

  • Many second order accurate nonoscillatory schemes are based on the minmod limiter, e.g., the Nessyahu-Tadmor scheme. It is well known that the L p -error of monotone finite difference methods for the linear advection equation is of order 1/2 for initial data in W 1 (L p ), 1 ≤ p ≤ ∞. 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 L2-error for a class of second order schemes based on the minmod limiter is of order at least 5/8 in contrast to the 1/2 order for any formally first order scheme. © 2006 American Mathematical Society.

author list (cited authors)

  • Popov, B., & Trifonov, O.

publication date

  • January 1, 2006 11:11 AM