Abstract: A front tracking method is used to construct weak solutions to scalar conservation laws with two kinds of boundary conditions --- Dirichlet conditions and a novel zero flux (or no-flow) condition. The construction leads to an efficient numerical method. The main feature of the scheme is that there is no stability condition correlating the spatial and temporal discretization parameters. The analysis uses the traditional method of proving compactness via Helly's theorem as well as the more modern concept of measure valued solutions. Three numerical examples are presented.
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