WEAK LOCAL RESIDUALS IN AN ADAPTIVE FINITE VOLUME METHOD FOR ONE-DIMENSIONAL SHALLOW WATER EQUATIONS

Sudi Mungkasi (Department of Mathematics, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002)
Stephen Gwyn Roberts (Mathematical Sciences Institute, The Australian National University,)

Journal of the Indonesian Mathematical Society
Volume 20 Number 1 (April 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