半线性抛物问题高效有限体积元法
The Efficient Finite Volume Element Methods for Semilinear Parabolic Equations
DOI: 10.12677/PM.2019.98122, PDF,    国家自然科学基金支持
作者: 熊之光, 王 易, 马 娟：湖南科技大学，数学与计算科学学院，湖南 湘潭
关键词: 半线性抛物方程；插值系数有限体积元；全离散格式；稳定性；Semilinear Parabolic Equations； Interpolation Coefficient Finite Volume Element； Totally Discrete Scheme； Stability
摘要: 本文研究了一类半线性抛物方程的有限体积元全离散格式。首先在空间上以插值系数线性有限体积元进行半离散，得到关于时间的一阶非线性常微分方程组的初值问题，然后在时间上采用向后差分方法得到全离散格式。其次讨论了该全离散格式的稳定性和收敛性。最后给出了一个数值例子说明所研究方法的高效性。
Abstract: In this paper, the fully discrete finite volume element schemes for a class of semi-linear parabolic equations are studied. Firstly, the initial value problem of the first-order nonlinear ordinary dif-ferential equations with time is obtained by interpolation coefficient finite volume element in space, and then the fully discrete scheme is obtained by backward difference method in time. Secondly, the stability and convergence of the fully discrete scheme are discussed. Finally, a numerical example is given to illustrate the efficiency of the proposed method.
文章引用：熊之光, 王易, 马娟. 半线性抛物问题高效有限体积元法[J]. 理论数学, 2019, 9(8): 961-968. https://doi.org/10.12677/PM.2019.98122

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