A new finite element approach for problems containing small geometric details
Wolfgang Hackbusch; Stefan A. Sauter
Archivum Mathematicum (1998)
- Volume: 034, Issue: 1, page 105-117
- ISSN: 0044-8753
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topHackbusch, Wolfgang, and Sauter, Stefan A.. "A new finite element approach for problems containing small geometric details." Archivum Mathematicum 034.1 (1998): 105-117. <http://eudml.org/doc/248183>.
@article{Hackbusch1998,
abstract = {In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization of PDEs without requiring periodicity of the data.},
author = {Hackbusch, Wolfgang, Sauter, Stefan A.},
journal = {Archivum Mathematicum},
keywords = {Finite Elements; Shortley-Weller discretization; complicated boundary; Shortley-Weller discretization; complicated boundary; micro-structures; composite finite elements; optimal interpolation order; computational complexity; stiffness matrix},
language = {eng},
number = {1},
pages = {105-117},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A new finite element approach for problems containing small geometric details},
url = {http://eudml.org/doc/248183},
volume = {034},
year = {1998},
}
TY - JOUR
AU - Hackbusch, Wolfgang
AU - Sauter, Stefan A.
TI - A new finite element approach for problems containing small geometric details
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 1
SP - 105
EP - 117
AB - In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete homogenization of PDEs without requiring periodicity of the data.
LA - eng
KW - Finite Elements; Shortley-Weller discretization; complicated boundary; Shortley-Weller discretization; complicated boundary; micro-structures; composite finite elements; optimal interpolation order; computational complexity; stiffness matrix
UR - http://eudml.org/doc/248183
ER -
References
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