A high order finite volume method for one dimensional nonlocal reactive flows of parabolic type |
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Authors: | Lejuan Wang Min Yang |
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Institution: | Department of Mathematics, School of Mathematics and Information Science, Yantai University, Yantai, Shandong, China |
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Abstract: | In this paper, we consider a high order finite volume approximation of one‐dimensional nonlocal reactive flows of parabolic type. The method is obtained by discretizing in space by arbitrary order vertex‐centered finite volumes, followed by a modified Simpson quadrature scheme for the time stepping. Compared to the existed finite volume methods, this new finite volume scheme could achieve the desired accuracy with less data storage by employing higher‐order trial spaces. The finite volume approximations are proved to possess optimal order convergence rates in the H1‐norm and L2‐norm, which are also confirmed by numerical tests. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | finite volume method high order nonlocal reactive flows parabolic |
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