@Article{CiCP-10-5,
author = {},
title = {Numerical Entropy and Adaptivity for Finite Volume Schemes},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1132--1160},
abstract = {<p style="text-align: justify;">We propose an a-posteriori error/smoothness indicator for standard semi-discrete
finite volume schemes for systems of conservation laws, based on the numerical
production of entropy. This idea extends previous work by the first author limited
to central finite volume schemes on staggered grids. We prove that the indicator converges
to zero with the same rate of the error of the underlying numerical scheme on
smooth flows under grid refinement. We construct and test an adaptive scheme for
systems of equations in which the mesh is driven by the entropy indicator. The adaptive
scheme uses a single nonuniform grid with a variable timestep. We show how
to implement a second order scheme on such a space-time non uniform grid, preserving
accuracy and conservation properties. We also give an example of a <em>p</em>-adaptive
strategy.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.250909.210111a},
url = {https://global-sci.com/article/80958/numerical-entropy-and-adaptivity-for-finite-volume-schemes}
}