Pointwise Error Estimates for Relaxation Approximations to Conservation Laws
Eitan Tadmor, Tao Tang
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Source: Crossref
Published: Jan 1, 2000
DOI: 10.1137/s0036141098349492
Open original source ↗Source abstract
We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip + stability). A one-sided interpolation inequality between classical L 1 error estimates and Lip + stability bounds enables us to convert a global L 1 result into a (nonoptimal) local estimate. Optimal error bounds on the weighted error then follow from the maximum principle for weakly coupled hyperbolic systems. The main difficulties in obtaining the Lip + stability and the optimal pointwise errors are how to construct appropriate "difference functions" so that the maximum principle can be applied.
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