| A New Finite Element Approach for Problems Containing Small Geometric Details (1998) | |||||||||||||||
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 e#cient 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. AMS Subject Classification. 65D05, 65N12, 65N15, 65N30, 65N50, 65N55 Keywords. Finite Elements, Shortley-Weller discretization, complicated boundary 1 Introduction Before the mid-sixties the finite di#erence method was the standard discretization method for di#erential equations. The following two severe drawbacks of finite di#erences lead to the development of the finite element method. First, the use of Cartesian di#erence quotients... | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||