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Volume 15, Issue 6
A Quadratic Finite Volume Method for Parabolic Problems

Yuanyuan Zhang & Xiaoping Liu

Adv. Appl. Math. Mech., 15 (2023), pp. 1407-1427.

Published online: 2023-10

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  • 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.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0313}, url = {http://global-sci.org/intro/article_detail/aamm/22046.html} }
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 -

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.

Zhang , Yuanyuan and Liu , Xiaoping. (2023). A Quadratic Finite Volume Method for Parabolic Problems. Advances in Applied Mathematics and Mechanics. 15 (6). 1407-1427. doi:10.4208/aamm.OA-2021-0313
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