@Article{CSIAM-AM-1-3,
author = {Li, Chen and Ruo, Li and Yang, Feng},
title = {An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2020},
volume = {1},
number = {3},
pages = {491--517},
abstract = {<p style="text-align: justify;">We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and applicable
on flexible grids. We show that the finite volume schemes with the new reconstruction
satisfy a local maximum principle with properly setup on time step length. Numerical examples are presented to show that the proposed scheme attains a third-order
accuracy for smooth solutions in both 2D and 3D cases. It is indicated by numerical
results that the local maximum principle is helpful to prevent overshoots in numerical
solutions.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.2020-0017},
url = {https://global-sci.com/article/82384/an-integrated-quadratic-reconstruction-for-finite-volume-schemes-to-scalar-conservation-laws-in-multiple-dimensions}
}