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The application of dual minimum theorems to the finite element solution of potential problems with special reference to seepage
Author(s) -
Ponter A. R. S.
Publication year - 1972
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.1620040110
Subject(s) - finite element method , mathematics , elasticity (physics) , boundary value problem , analogy , element (criminal law) , potential energy , class (philosophy) , calculus (dental) , mathematical optimization , mathematical analysis , computer science , structural engineering , engineering , classical mechanics , linguistics , medicine , philosophy , physics , dentistry , political science , law , materials science , artificial intelligence , composite material
Abstract By formulating the potential boundary value problems in terms of physical (in contrast to purely mathematical) variables, the existence of dual energy principles may be clearly distinguished. In direct analogy with elasticity, two possible energy methods present themselves giving rise to two possible finite element procedures. General upper and lower bounds on an energy quantity may be obtained, which in the case of seepage become the total seepage rate for a certain class of seepage problem. For this case of seepage the derivation of the finite element procedure and the computing of the bounds is described.