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A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

  • Christos Xenophontos EMAIL logo

Abstract

We consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree p3 defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

MSC 2010: 65N30

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Received: 2016-9-9
Revised: 2016-12-9
Accepted: 2016-12-15
Published Online: 2017-1-10
Published in Print: 2017-4-1

© 2017 by De Gruyter

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