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On the Full and Global Accuracy of a Compact Third Order WENO Scheme: Part II

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Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 112)

Abstract

Recently, we showed in (O. Kolb, SIAM J. Numer. Anal., 52 (2014), pp. 2335–2355) for which parameter range the compact third order WENO reconstruction procedure introduced in (D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 22 (2000), pp. 656–672) reaches the optimal order of accuracy (h3 in the smooth case and h2 near discontinuities). This is the case for the parameter choice ɛ = Kh q in the weight design with q ≤ 3 and pq ≥ 2, where p ≥ 1 is the exponent used in the computation of the weights in the WENO scheme. While these theoretical results for the convergence rates of the WENO reconstruction procedure could also be validated in the numerical tests, the application within the semi-discrete central scheme of (A. Kurganov, and D. Levy, SIAM J. Sci. Comput., 22 (2000), pp. 1461–1488) together with a third order TVD-Runge-Kutta scheme for the time integration did not yield a third order accurate scheme in total for q > 2. The aim of this follow-up paper is to explain this observation with further analytical and numerical results.

Keywords

Weighted Essentially Non-oscillatory (WENO) WENO Scheme Order WENO WENO Reconstruction Reconstruction Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MannheimMannheimGermany

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