A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems
Date
2017ISSN
1609-4840Source
Computational Methods in Applied MathematicsVolume
17Issue
2Pages
337-349Google Scholar check
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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 p ≥ 3 p≥q 3 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. © 2017 by De Gruyter.
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