Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems

Details Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems

2011-01-06

arxiv.org/abs/1101.1218v1

Mathematics

Numerical Analysis

Scientific paper

This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a $C^0$ extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results.

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