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Mathematics of Computation

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TVB uniformly high-order schemes for conservation laws

Author: Chi-Wang Shu
Journal: Math. Comp. 49 (1987), 105-121
MSC: Primary 65M05; Secondary 35L65, 65M10
MathSciNet review: 890256
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Abstract: In the computation of conservation laws ${u_t} + f{(u)_x} = 0$, TVD (total-variation-diminishing) schemes have been very successful. But there is a severe disadvantage of all TVD schemes: They must degenerate locally to first-order accuracy at nonsonic critical points. In this paper we describe a procedure to obtain TVB (total-variation-bounded) schemes which are of uniformly high-order accuracy in space including at critical points. Together with a TVD high-order time discretization (discussed in a separate paper), we may have globally high-order in space and time TVB schemes. Numerical examples are provided to illustrate these schemes.

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Article copyright: © Copyright 1987 American Mathematical Society