The engineer grapples with Theorem 1.1 and Lemma 6.3 of Strang and Fix

The best-known statements on error analysis of the finite element method are derived using rigorous mathematical abstractions which are difficult for the average engineer (who remains the biggest user) to grasp. There is much merit in being able to re-derive these using the energy, virtual work and...

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Bibliographic Details
Published in:Current science (Bangalore) 2003-10, Vol.85 (7), p.989-994
Main Authors: Prathap, G., Mukherjee, S.
Format: Article
Language:English
Subjects:
Aerospace engineering
Differential equations
Eigenvalues
Elastodynamics
Elastostatics
Error rates
Finite element method
Inner products
Mathematical theorems
Matrices
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Summary:The best-known statements on error analysis of the finite element method are derived using rigorous mathematical abstractions which are difficult for the average engineer (who remains the biggest user) to grasp. There is much merit in being able to re-derive these using the energy, virtual work and least action principles that the engineer or physicist is more familiar with. In this article, we attempt to do this, to obtain Theorem 1.1 and Lemma 6.3 of Strang and Fix, perhaps the most valuable of all error statements ever made of finite element elastostatics and elastodynamics. We also looked at some interesting atypical problems which arise when errors that appear when finite element discretization is used to solve problems of interest in engineering and applied science are studied. The formal mathematical theorems and lemmas which have been identified in the seminal work of Strang and Fix, are now re-examined for these atypical situations using an engineering approach.
ISSN:0011-3891