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In this paper, which i s a c o n tinuation of 20], 21], 22] and 24], we present a shock tracking technique in one space dimension. The main feature of the technique is that it uses the conservativity of the hyperbolic conservation laws rather than the Hugoniot condition to track discontinuities. Roughly speaking, the technique is as follows: The computation of a numerical solution on each side of a discontinuity uses information only from the same side. This can be done by employingdoi:10.3929/ethz-a-004283832 fatcat:wyfwrbpnojco7kab2n66pp4iby