@Article{CSIAM-AM-1-491, author = {Li and Chen and and 9153 and and Li Chen and Ruo and Li and and 9154 and and Ruo Li and Feng and Yang and and 9155 and and Feng Yang}, 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 = {

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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0017}, url = {http://global-sci.org/intro/article_detail/csiam-am/18305.html} }