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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.
Key words. Adaptive finite element methods, scientific software, software design.
AMS subject classification. 65N30, 65N50, 65Y15
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