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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Negative Norm Estimates and Superconvergence
verfasst von : Vidar Thomée
Erschienen in: Galerkin Finite Element Methods for Parabolic Problems
Verlag: Springer Berlin Heidelberg
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In this chapter we shall extend our earlier error estimates in
L
2
and
H
1
to estimates in norms of negative order. It will turn out that if the accuracy in
L
2
of the family of approximating spaces is
O
(
h
r
) with
r
> 2, then the error bounds in norms of negative order is of higher order than
O
(
h
r
). In certain situations these higher order bounds may be applied to show error estimates for various quantities of these higher orders, so called
superconvergent
order estimates. We shall exemplify this by showing how certain integrals of the solution of the parabolic problem, and, in one space dimension, the values of the solution at certain points may be calculated with high accuracy using the semidiscrete solution.