Localization effects and measure source terms in numerical schemes for balance laws
Mathematics of Computation
On accuracy of adaptive grid methods for captured shocks
Journal of Computational Physics
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
Mathematics of Computation
Journal of Scientific Computing
Error localization in solution-adaptive grid methods
Journal of Computational Physics
Short Note: Interaction of a shock with a density disturbance via shock fitting
Journal of Computational Physics
Second-order Godunov-type scheme for reactive flow calculations on moving meshes
Journal of Computational Physics
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
Journal of Computational Physics
An investigation of the internal structure of shock profiles for shock capturing schemes
Journal of Computational and Applied Mathematics
Shock Capturing Artificial Dissipation for High-Order Finite Difference Schemes
Journal of Scientific Computing
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Finite difference approximations generically have ${\cal O}(1)$ pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.