WEAK LOCAL RESIDUALS IN AN ADAPTIVE FINITE VOLUME METHOD FOR ONE-DIMENSIONAL SHALLOW WATER EQUATIONS - Sudi Mungkasi; Stephen Gwyn Roberts (Journal of the Indonesian Mathematical Society, 2014)
Weak local residual (WLR) detects the smoothness of numerical solutionsto conservation laws. In this paper we consider balance laws with a sourceterm, the shallow water equations (SWE). WLR is used as the reﬁnement indicatorin an adaptive ﬁnite volume method for solving SWE. This is the ﬁrst studyin implementing WLR into an adaptive ﬁnite volume method used to solve theSWE, where the adaptivity is with respect to its mesh or computational grids. Welimit our presentation to one-dimensional domain. Numerical simulations show theeﬀectiveness of WLR as the reﬁnement indicator in the adaptive method.DOI : http://dx.doi.org/10.22342/jims.20.1.176.11-18