A Quadratic Finite Volume Method for Parabolic Problems

A Quadratic Finite Volume Method for Parabolic Problems

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.

Author Details

Yuanyuan Zhang

Xiaoping Liu