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Treatment of material discontinuity in two meshless local Petrov–Galerkin (MLPG) formulations of axisymmetric transient heat conduction
Author(s) -
Batra R. C.,
Porfiri M.,
Spinello D.
Publication year - 2004
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.1156
Subject(s) - petrov–galerkin method , discontinuity (linguistics) , mathematics , thermal conduction , mathematical analysis , rotational symmetry , heat flux , quadrature (astronomy) , jump , finite element method , geometry , mechanics , physics , heat transfer , thermodynamics , optics , quantum mechanics
We use two meshless local Petrov–Galerkin (MLPG) formulations to analyse heat conduction in a bimetallic circular disk. The continuity of the normal component of the heat flux at the interface between two materials is satisfied either by the method of Lagrange multipliers or by using a jump function. The convergence of the H 0 and H 1 error norms for the four numerical solutions with an increase in the number of equally spaced nodes and in the number of quadrature points is scrutinized. With an increase in the number of uniformly spaced nodes, the two error norms decrease monotonically for the MLPG5 formulation but are essentially unchanged for the MLPG1 formulation. To our knowledge, this is the first study comparing the performance of the two methods of modelling a discontinuity in the gradient of a field variable at the interface between two different materials. Copyright © 2004 John Wiley & Sons, Ltd.