Achievements and some unsolved problems of the finite element method

After outlining the early history of the finite element method the paper concentrates on to (1) some important achievements of the last decade and (2) presents an outline of some problems still requiring treatement. In the first part, the developments of the patch test for assessment of elements, ne...

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Published inInternational journal for numerical methods in engineering Vol. 47; no. 1-3; pp. 9 - 28
Main Author Zienkiewicz, O. C.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 10.01.2000
Subjects
adaptive refinement
CBS algorithm
finite element method
fluid dynamics
patch test
Online AccessGet full text
ISSN0029-5981
1097-0207
DOI10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P

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Abstract After outlining the early history of the finite element method the paper concentrates on to (1) some important achievements of the last decade and (2) presents an outline of some problems still requiring treatement. In the first part, the developments of the patch test for assessment of elements, new developments of adaptive refinement and the principles of the general CBS algorithm for fluid dynamics are presented. Copyright © 2000 John Wiley & Sons, Ltd.
AbstractList After outlining the early history of the finite element method the paper concentrates on to (1) some important achievements of the last decade and (2) presents an outline of some problems still requiring treatement. In the first part, the developments of the patch test for assessment of elements, new developments of adaptive refinement and the principles of the general CBS algorithm for fluid dynamics are presented. Copyright © 2000 John Wiley & Sons, Ltd.
After outlining the early history of the finite element method, the paper concentrates on some important achievements of the last decade and presents an outline of some problems still requiring treatment. In the first part, the developments of the patch test for assessment of elements, new developments of adaptive refinement and the principles of the general CBS algorithm for fluid dynamics are presented.
Following a brief development history of the FEM, a development status for the method is conducted which gives attention to the 'patch test' for elements-assessment, recent developments in adaptive grid refinement, and the principles of the general characteristics-based split algorithm for fluid mechanics. Also discussed are unresolved problems in CFD uses of the FEM relevant to aerodynamics. (AIAA)
Author Zienkiewicz, O. C.
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Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB56) 1998
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Taylor (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB19) 1986; 22
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB21) 1997; 149
Huang (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB25) 1984; 1
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB16) 1989; I
Xu (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB30) 1986; 2
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Southwell (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB7B) 1940
Courant (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB11) 1953; I
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB2) 1947; 27
Clough (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB18) 1965
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB50) 1984; 5
Argyris (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB9) 1960
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB34) 1992; 24
Taylor (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB29) 1993; 36
Morton (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB49) 1985; 52
Southwell (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB8) 1946; I
Babu?ka (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB32) 1978; 11
Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB52) 1995; 20
Babu?ka (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB33) 1979; 17/18
Satya Sai (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB55) 1998; 27
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Zienkiewicz (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB27) 1988
Lax (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB42) 1960; 13
Babu?ka (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB40) 1994; 37
Ewing (10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P-BIB45) 1981; IV
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Snippet After outlining the early history of the finite element method the paper concentrates on to (1) some important achievements of the last decade and (2) presents...
Following a brief development history of the FEM, a development status for the method is conducted which gives attention to the 'patch test' for...
After outlining the early history of the finite element method, the paper concentrates on some important achievements of the last decade and presents an...
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SubjectTerms adaptive refinement
CBS algorithm
finite element method
fluid dynamics
patch test
Title Achievements and some unsolved problems of the finite element method
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