Volume 51, pp. 50-62, 2019.

Numerical treatment of singularly perturbed fourth-order two-parameter problems

Mirjana Brdar, Sebastian Franz, and Hans-Görg Roos

Abstract

A singularly perturbed fourth-order problem with two small parameters is considered in one dimension and on a smooth domain in two dimensions. Using its discretisation by a mixed finite element method on a properly defined Shishkin mesh, we prove convergence in the associated energy norm.

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Key words

singular perturbation, fourth-order problem, two small parameters, mixed method, layer-adapted meshes

AMS subject classifications

65L11, 65L60, 65N30, 65N50

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