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In this work the control volume finite element (cvfe) method is used to discretise a two-dimensional non-linear transport model on an unstructured mesh. First and second order temporal weighting, combined with various flux limiting techniques (spatial weighting) are analysed in order to identify the most accurate and efficient numerical scheme. An inexact Newton method is used to resolve the underlying discrete non-linear system. In computing the Newtondoi:10.21914/anziamj.v44i0.706 fatcat:rmi76cwv2fcdtplrdwep3ybumm