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On the importance of the discrete maximum principle in transient analysis using finite element methods
Author(s) -
Rank Ernst,
Katz Casimir,
Werner Heinrich
Publication year - 1983
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.1620191205
Subject(s) - discretization , transient (computer programming) , finite element method , stability (learning theory) , limit (mathematics) , mathematics , maximum principle , space (punctuation) , mathematical analysis , calculus (dental) , mathematical optimization , computer science , engineering , structural engineering , dentistry , machine learning , medicine , optimal control , operating system
In transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.