A nonconforming finite element method for a singularly perturbed boundary value problem (Q1343676)

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.