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A new finite element approach for problems containing small geometric details. (English) Zbl 0912.65088

The authors present a new finite element technique to examine domains containing small micro-structures. To this end they introduce the so-called composite finite elements. The main theorem establishes the optimal interpolation order of the proposed elements in the \(L^2\)- and \(H^1\)-norm. Computational complexity of generating the stiffness matrix is discussed.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
74A60 Micromechanical theories
74M25 Micromechanics of solids
74S05 Finite element methods applied to problems in solid mechanics
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