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Singularly perturbed finite element methods. (English) Zbl 0569.65065
The paper deals with the approximation of singularly perturbed ordinary differential equations by new piecewise linear finite elements (hinged elements). The purpose of introducing one or more hinges into a standard element is to allow the element to modify itself as the perturbation parameter \(\epsilon\) changes. As a result, pointwise and global error estimates (independent of \(\epsilon)\) are presented.
Reviewer: J.Haslinger

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
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