Zusammenfassung
We consider finite elements that are adapted to a (semi)norm that
is weaker than the one of the trial space. We establish convergence
of the finite element solutions to the exact one under the following
conditions: refinement relies on unique quasi-regular element subdivisions
and generates locally quasi-uniform grids; the finite element spaces
are conforming, nested, and satisfy the inf-sup condition; the error
estimator is reliable and appropriately locally efficient; the indicator
of a non-marked element is bounded by the estimator contribution
associated with the marked elements, and each marked element is subdivided
at least once. This abstract convergence result is illustrated by
two examples.
Nutzer