Constructive error analysis of a full-discrete finite element method for the heat equation

被引：4

作者：

Hashimoto, Kouji ^{[1
]}

Kimura, Takuma ^{[2
]}

Minamoto, Teruya ^{[2
]}

Nakao, Mitsuhiro T. ^{[3
]}

机构：

[1] Nakainum Ciakuen Jr Coll, Div Infant Educ, Fukuoka, Fukuoka 8140198, Japan

[2] Saga Univ, Dept Informat Sci, Saga 8408502, Japan

[3] Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2019年 / 36卷 / 03期

关键词：

Constructive error analysis; Finite element method; Heat equation;

D O I：

10.1007/s13160-019-00362-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：777 / 790

页数：14

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