Constructive error estimates for full discrete approximation of periodic solution for heat equation
Constructive error estimates for full discrete approximation of periodic solution for heat equation
复制标题
热方程周期解的全离散近似的建设性误差估计
DOI：
10.1016/j.cam.2019.112510
复制
发表时间：
2020
影响因子：
2.4
通讯作者：
Nakao Mitsuhiro T.
中科院分区：
文献类型：
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作者：
Kimura Takuma;Minamoto Teruya;Nakao Mitsuhiro T.
考虑了具有时间周期条件的热传导方程全离散数值解的构造性先验误差估计。我们的数值方案是基于有限元半离散化在空间方向上结合插值的时间使用的基本矩阵的半离散化问题。本文给出了非线性抛物型方程精确解的数值验证方法中的最优阶H1和L2误差估计。几个数值例子，确认的最佳收敛速度。
We consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation with time-periodic condition. Our numerical scheme is based on the finite element semidiscretization in space direction combined with an interpolation in time using the fundamental matrix for the semidiscretized problem. We derive the optimal order H 1 and L 2 error estimates that are critical in the numerical verification method of exact solutions for nonlinear parabolic equations. Several numerical examples that confirm the optimal rate of convergence are presented.