We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has O(Δ x) errors, improving over O(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.
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Glimm et al. (2003) studied this question.
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