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Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem

Bill Semper
SIAM Journal on Numerical Analysis
Vol. 29, No. 4 (Aug., 1992), pp. 1043-1058
Stable URL: http://www.jstor.org/stable/2157990
Page Count: 16
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Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem
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Abstract

Conforming Galerkin approximations to a singularly perturbed fourth-order partial differential equation are examined. Global and local error estimates are derived. In the case when the perturbation parameter is much smaller than the mesh size, the Galerkin procedure is seen to behave poorly, even locally.

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