论文信息 - A nonconforming finite element method for a singularly perturbed boundary value problem

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

We analyze 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 orderh1/2 in a norm slightly stronger than the energy norm. Our proof uses a new abstract convergence theorem for Petrov-Galerkin finite element methods.ZusammenfassungWir analysieren eine neue nichtkonforme Petrov-Galerkin Finite-Elemente-Methode zur Lösung eines linearen singulär gestörten 2-Punkt Randwertproblems ohne Wendepunkte. In einer im Vergleich zur üblichen Engergienorm etwas stärkeren Norm wird gezeigt, daß die Methode bezüglich des Störparameters gleichmäßig konvergent mit der Ordnungh1/2 ist. Unser Beweis benutzt ein neues abstraktes Konvergenztheorem für Petrov-Galerkin Finite-Elemente-Methoden.

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