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Application of essential boundary conditions in mesh‐free methods: a corrected collocation method
Author(s) -
Wagner Gregory J.,
Liu Wing Kam
Publication year - 2000
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/(sici)1097-0207(20000320)47:8<1367::aid-nme822>3.0.co;2-y
Subject(s) - discretization , collocation (remote sensing) , collocation method , boundary (topology) , mathematics , singular boundary method , orthogonal collocation , convergence (economics) , boundary value problem , matrix (chemical analysis) , mathematical analysis , computer science , finite element method , differential equation , boundary element method , ordinary differential equation , engineering , structural engineering , machine learning , materials science , economic growth , economics , composite material
Collocation methods for applying essential boundary conditions are defined as those methods in which conditions are enforced exactly at a discrete set of boundary nodes. In mesh‐free methods, this is usually accomplished by replacing rows of the matrix equations which result from discretization of the weak form with equations which ensure the enforcement of boundary conditions. In this paper, an inconsistency in this method is pointed out, and a correction is derived. Numerical test are done on one‐ and two‐dimensional equations; it is shown that convergence rates decrease with the use of the invalid traditional collocation and are restored with the corrected method. Copyright © 2000 John Wiley & Sons, Ltd.