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Berger, M.J. and Oliger, J. (1984) Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. Journal of Computational Physics, 53, 484-512.
https://doi.org/10.1016/0021-9991(84)90073-1

has been cited by the following article:

• TITLE: Postshock Oscillations on Non-Uniform Mesh

  AUTHORS: Fuxing Hu

  KEYWORDS: Nonuniform Mesh, Hyperbolic Conservation Laws, Postshock Oscillation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.2, February 24, 2017

  ABSTRACT: An investigation of postshock oscillations on non-uniform grids is performed in this paper. These oscillations are generated as shock passes through the grid interfaces. The LLF scheme is checked for 1D and 2D problems on the discontinuous grids. Oscillations are observed only for nonlinear systems and the solutions of the scalar conservation laws and linear systems behave logically. The integral curves suggest underlying properties of these oscillations. The results of the paper reveal a flaw that adaptive methods for conservation laws have to refine grids at each time step.