Error estimates for the approximation of semicoercive
variational inequalities |
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Authors: | W Spann |
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Institution: | (1) Mathematisches Institut der Universit\"at M\"unchen, Theresienstrasse 39, D-80333 M\"unchen, Germany , DE |
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Abstract: | Summary.
An abstract error estimate for the approximation of semicoercive variational
inequalities is obtained provided a certain condition holds for the exact
solution. This condition turns out to be necessary as is demonstrated
analytically and numerically. The results are applied to the finite element
approximation of Poisson's equation with Signorini boundary conditions
and to the obstacle problem for the beam with no fixed boundary conditions.
For second order variational inequalities the condition is always satisfied,
whereas for the beam problem the condition holds if the center of forces
belongs to the interior of the convex hull of the contact set. Applying the error
estimate yields optimal order of convergence in terms of the mesh size
.
The numerical convergence rates observed are in good agreement with the
predicted ones.
Received August 16, 1993 /
Revised version received March 21, 1994 |
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Keywords: | Mathematics Subject Classification (1991):65K10 65N30 49J40 |
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