# 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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