Premium
Finite elements formulated by the weighted discrete least squares method
Author(s) -
Lynn Paul P.,
Arya Santosh K.
Publication year - 1974
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620080107
Subject(s) - mathematics , finite element method , smoothing , constant (computer programming) , convergence (economics) , minification , least squares function approximation , method of mean weighted residuals , square (algebra) , differential equation , relaxation (psychology) , mixed finite element method , mathematical analysis , mathematical optimization , geometry , computer science , galerkin method , psychology , social psychology , statistics , estimator , economics , thermodynamics , programming language , economic growth , physics
By use of the least squares error criterion, an alternate finite element formulation is presented. The method is based on the discrete or element‐wise minimization of square and weighted differential equation residuals which are expressed in terms of element nodal quantities. In order to overcome the stringent inter‐element continuity requirement, a major stumbling block, on the element trial functions two practical schemes are proposed. One is the reduction of the original governing differential equation to a system of equivalent first order differential equations; the other is a method of smoothing discontinous trial functions. The latter essentially relaxes the continuity requirement and yields efficient non‐conforming finite elements. This paper also demonstrates the use of constant weights which significantly improves the rates of convergence. Several numerical examples illustrate the proposed method. From these examples, it may be concluded that the use of constant weights and the relaxation of the inter‐element continuity requirement are two indispensable features of the weighted discrete least square method.