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Talk Abstract

A general concept for adaptivity in finite element methods

A general concept for adaptivity in finite element methods

The conventional strategy for controlling the error in finite-element
methods is based on * a posteriori* estimates for the error
in the global "energy" or *L _{2}*-norm involving
local residuals of the computed solution. Such estimates contain
constants describing the local approximation properties of the
finite-element space and the stability properties of a linearized
dual problem. The mesh refinement then aims at equilibrating
the local error indicators. However, meshes generated in this
way via controlling the error in a global norm may not be appropriate
for local error quantities like point values or contour integrals,
and in the case of strongly varying coefficients. This deficiency
may be overcome by introducing weight factors in the

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