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On the SHASTA FCT algorithm for the equation $ \partial \rho /\partial \ t+(\partial /\partial x)(v(\rho )\,\rho )=0$

Authors: Tsutomu Ikeda and Tomoyasu Nakagawa
Journal: Math. Comp. 33 (1979), 1157-1169
MSC: Primary 65M05; Secondary 35L65, 65M10
MathSciNet review: 537963
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Abstract: In recent years, Boris, Book and Hain have proposed a family of finite difference methods called FCT techniques for the Cauchy problem of the continuity equation. The purpose of this paper is to study the stability and convergence about the SHASTA FCT algorithm, which is one of the basic schemes among many FCT techniques, though not in its original form but a slightly modified one for our technical reason. (Our numerical experiments indicate less distinction between the algorithm dealt with here and the original SHASTA FCT one in terms of reproduction of sharp discontinuities.) The main results are Theorems 1 and 2 concerning the $ {L^\infty }$-stability and the $ L_{{\operatorname{loc}}}^1$-convergence, respectively.

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Keywords: Conservation law, generalized solution, entropy condition, positive finite difference scheme, Flux-Corrected Transport (FCT) technique, antidiffusion operator, SHASTA, $ {L^\infty }$-stability, $ L_{{\operatorname{loc}}}^1$-convergence, function having locally bounded variation, schemes in conservation form
Article copyright: © Copyright 1979 American Mathematical Society