Constructive error analysis of a fulldiscrete finite element method for the heat equations
Constructive error analysis of a fulldiscrete finite element method for the heat equations
复制标题
热方程全离散有限元法的构造误差分析
DOI：
10.1007/s13160-019-00362-6
复制
发表时间：
2019
影响因子：
0.9
通讯作者：
M.T.
中科院分区：
文献类型：
--
作者：
Hashimoto;K.;Kimura;T.;Minamoto;T.;Nakao;M.T.
提出了一种新的热方程全离散有限元方法，并通过计算验证了该方法的数值稳定性。由于在误差分析中，我们使用了Nakao等人提出的建设性误差估计（SIAM J num Anal 51(3): 1525-1541, 2013），因此这项工作被认为是对该论文的扩展。我们强调，与以前的方案相比，有关方案似乎使用了相当标准的伽辽金方法，并且易于实现进化方程。在构造误差估计中，我们有效地使用了数值计算，保证了精度。
We present a new full-discrete finite element method for the heat equation, and show the numerical stability of the method by verified computations. Since, in the error analysis, we use the constructive error estimates proposed by Nakao et al. (SIAM J Numer Anal 51(3):1525–1541, 2013) this work is considered as an extension of that paper. We emphasize that the concerned scheme seems to use the quite standard Galerkin method and is easy to implement for evolutionary equations compared with previous ones. In the constructive error estimates, we effectively use the numerical computations with guaranteed accuracy.