Adaptive finite element methods are a modern, widely used tool which
make realistic computations feasible, even in three space dimensions.
We describe the basic ideas and ingredients of adaptive FEM and the
implementation of our toolbox \ALBERT. The design of \ALBERT is based
on the natural hierarchy of locally refined meshes and an abstract
concept of general finite element spaces. As a result, dimension
independent programming of applications is possible. Numerical results
from applications in two and three space dimensions demonstrate the
flexibility of \ALBERT.
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