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On the error behavior of the reduced basis technique for nonlinear finite element approximations. (English) Zbl 0533.73071
The reduced basis method consists of a special selection of approximating bases (or subspaces) for the solution of boundary value problems. The basis functions may be viewed as the first few coordinate directions of a ”moving frame” along the solution. For finite element approximations the method results in a significant reduction in size (of the stiffness equations). Frequently, only few (globally defined) basis functions, derived from the shape functions, suffice for obtaining a solution. This paper outlines the theoretical foundation of the reduced basis method. The existence of solutions for the original problem and of the reduced basis approximation are treated. Estimation of the reduced basis errors is derived, giving reasons for the effectiveness of the method. A particular problem serves for illustrating the method.
Reviewer: Sh.Ginsberg

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
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