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A logic for simple Petrov–Galerkin weighting functions
Author(s) -
Freund J.,
Salonen E.M.
Publication year - 1992
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.1620340308
Subject(s) - weighting , petrov–galerkin method , simple (philosophy) , boundary value problem , jump , mathematics , point (geometry) , galerkin method , calculus (dental) , mathematical analysis , mathematical optimization , finite element method , geometry , engineering , physics , acoustics , medicine , philosophy , structural engineering , epistemology , dentistry , quantum mechanics
Weak form for the solution of the complete second order boundary value problem in one‐dimensional case is derived in a way, which should be easy to comprehend. The starting point is the boundary value problem extended with suitable jump conditions. The aim is a convenient form for numerical calculations and weighting functions giving accurate nodal values. The connections with SUPG‐, GLS‐ and GGLS‐method is discussed with reinvention explaining the selections of ‘free’ parameters related to these methods. Finally some ideas to extend the methods to two‐dimensional cases are presented.