TY - JOUR
T1 - A Quadratic Finite Volume Method for Parabolic Problems
AU - Zhang , Yuanyuan
AU - Liu , Xiaoping
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1407
EP - 1427
PY - 2023
DA - 2023/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0313
UR - https://global-sci.org/intro/article_detail/aamm/22046.html
KW - Higher-order finite volume method, parabolic problems, error estimate.
AB - <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>