@Article{AAMM-15-1407,
author = {Zhang , Yuanyuan and Liu , Xiaoping},
title = {A Quadratic Finite Volume Method for Parabolic Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {6},
pages = {1407--1427},
abstract = {<p style="text-align: justify;">In this paper, a quadratic finite volume method (FVM) for parabolic problems is studied. We first discretize the spatial variables using a quadratic FVM to
obtain a semi-discrete scheme. We then employ the backward Euler method and the
Crank-Nicolson method respectively to further disctetize the time vatiable so as to
derive two full-discrete schemes. The existence and uniqueness of the semi-discrete
and full-discrete FVM solutions are established and their optimal error estimates are
derived. Finally, we give numerical examples to illustrate the theoretical results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0313},
url = {http://global-sci.org/intro/article_detail/aamm/22046.html}
}