Yamamoto's principle and its applications to precise finite element error analysis.
type: Item
instance of: scholarly article
title: Yamamoto's principle and its applications to precise finite element error analysis.
zbMATH Open document ID: 1041.65063
DOI: 10.1016/S0377-0427(02)00727-6
author: Takuya Tsuchiya
author: Kazuki Yoshida
author: Sae Ishioka
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-19T00:00:00Z
review text: The paper is concerned with boundary value problems of linear second-order ordinary differential equations boundary value problems with non-coercive principal part, and with linear spline (finite element) methods for their approximation. The main goal is to derive error bounds similar to those known for coercive problems. Here, the essential work consists in obtaining such bounds for the auxiliary problem where the non-principal part is set to zero. For this problem, the Green function is known in closed form; this enables a precise comparison between the inverses of the continuous (differential) and the discrete (finite element) operator, and thus, the desired error bounds. By a compactness argument, the non-principal part is also taken into account, Finally, error bounds for the derivative at the nodal points are derived.
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 1912290
zbMATH Keywords: two-point boundary value problem
zbMATH Keywords: non-coercive
zbMATH Keywords: linear splines
zbMATH Keywords: error bounds
zbMATH Keywords: Green function
zbMATH Keywords: finite elements
zbMATH Keywords: Yamamoto's principle
reviewed by: Michael Plum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1912290