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A-posteriori error estimates for systems of hyperbolic conservation laws (2305.01340v1)
Published 2 May 2023 in math.NA and cs.NA
Abstract: We provide rigorous and computable a-posteriori error estimates for first order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by Bressan, Chiri and Shen and a novel method to compute negative order norms of residuals. Numerical experiments show that the error estimator converges with the rate predicted by a-priori error estimates.