Tau-lines: A new hybrid approach to the numerical treatment of crack problems based on the Tau method
type: Item
instance of: scholarly article
title: Tau-lines: A new hybrid approach to the numerical treatment of crack problems based on the Tau method
zbMATH Open document ID: 0576.73095
DOI: 10.1016/0045-7825(86)90042-3
author: A. E. M. El Misiery
author: Eduardo L. Ortiz
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1986-01-01T00:00:00Z
review text: A new hybrid computaional technique based on Ortiz' recursive formulation of the Tau method is introduced in this paper and applied to some model singular boundary value problems which are relevant to fracture mechanics (modes I and III). This technique, which we call Tau-lines, combines the method of lines with the Tau method. The former is used in the construction of a system of coupled ordinary differential equations which is the discretized model of a given partial differential equation; the latter is used to find an accurate approximation of the solution of such a system which involves no further discretization. Recent theoretical results on the Tau method show that its error is optimal in the sense that, for a given degree n, it has the same order of error as the best uniform approximation of the exact solution by algebraic polynomials of degree n. The present work may be considered as an encouraging first step towards the development of the Tau-lines approach into a useful and efficient computational tool for the numerical treatment of problems in fracture mechanics.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 65N99
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 3922151
zbMATH Keywords: hybrid computational technique
zbMATH Keywords: Ortiz' recursive formulation of the Tau method
zbMATH Keywords: singular boundary value problems
zbMATH Keywords: modes I and III
zbMATH Keywords: Tau-lines
zbMATH Keywords: method of lines
zbMATH Keywords: system of coupled ordinary differential equations
zbMATH Keywords: discretized model of a given partial differential equation
zbMATH Keywords: accurate approximation
MaRDI profile type: Publication
full work available at URL: 0045-7825(86)90042-3
OpenAlex ID: W2043329627
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description: scientific article; zbMATH DE number 3922151