Geodesic
A new finite element approach for problems containing small geometric details
Archivum mathematicum, Tome 34 (1998) no. 1, pp. 105-117

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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.
Classification : 65N15, 65N30, 65N50, 65Y20, 74A60, 74M25, 74S05
Keywords: Finite Elements; Shortley-Weller discretization; complicated boundary 
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     author = {Hackbusch, W. and Sauter, S.},
     title = {A new finite element approach for problems containing small geometric details},
     journal = {Archivum mathematicum},
     pages = {105--117},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1998},
     mrnumber = {1629676},
     zbl = {0912.65088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a10/}
}
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Hackbusch, W.; Sauter, S. A new finite element approach for problems containing small geometric details. Archivum mathematicum, Tome 34 (1998) no. 1, pp. 105-117. http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a10/