 
Summary: Numer. Math. 37, 405421 (1981) Numerische
Mathematik
@ SpringerVerlag1981
Discretization by Finite Elements
of a Model Parameter Dependent Problem
Douglas N. Arnold
Department of Mathematicsand Institute for PhysicalScienceand Technology.
Universityof Maryland,ColIegePark, MaryIand 20742, USA
Abstract. The discretization by finite elements of a model variational prob
lem for a clamped loaded beam is studied with emphasis on the effect of
the beam thickness, which appears as a parameter in the problem, on the
accuracy. It is shown that the approximation achieved by a standard finite
element method degenerates for thin beams. In contrast a large family of
mixed finite element methods are shown to yield quasioptimal approxima
tion independent of the thickness parameter. The most useful of these
methods may be realized by replacing the integrals appearing in the stiff
ness matrix of the standard method by Gauss quadratures.
Subject Classifications: AMS(MOS): 65N30; CR: 5.17.
1. Introduction
In this paper we examine the finite element discretization of a model vari
