Order of convergence of second order schemes based on the minmod limiter |
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| Authors: | Bojan Popov Ognian Trifonov. |
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| Affiliation: | Department of Mathematics, Texas A&{M} University, College Station, Texas 77845 ; Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208 |
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| 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  -error of monotone finite difference methods for the linear advection equation is of order  for initial data in  ,  . 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  -error for a class of second order schemes based on the minmod limiter is of order at least  in contrast to the  order for any formally first order scheme. |
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| Keywords: | Conservation laws error estimates second order schemes minmod limiter |
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