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A nonconforming finite element method for a singularly perturbed boundary value problem. (English) Zbl 0813.65105
This paper analyzes a new nonconforming Petrov-Galerkin finite element method for solving linear singularly perturbed two-point boundary value problems without turning points. The method is shown to be convergent, uniformly in the perturbation parameter, of order \(h^{1/2}\) in a norm slightly stronger than the energy norm. The proof uses a new abstract convergence theorem for Petrov-Galerkin finite element methods.

MSC:
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 for ordinary differential equations
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