Year: 2023
Author: Yuanyuan Zhang, Xiaoping Liu
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1407–1427
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0313
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1407–1427
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Higher-order finite volume method parabolic problems error estimate.