Abstract data structures for a finite element package: Design principles of ALBERT

ALBERT is an Adaptive multi-Level finite element toolbox using Bisectioning refinement and Error control by Residual Techniques. Its design is based o n appropriate data structures holding geometrical, finite element, and alge braic information. Using such data structures, abstract adaptive methods fo r stationary and time dependent problems, assembly tools for discrete syste ms, and dimension dependent tasks like mesh modifications can be provided i n a library. This allows dimension-independent development and programming of a general class of applications. In ALBERT, hierarchical 2d and 3d meshe s are stored in binary trees. Several sets of finite elements can be used o n the same mesh, either using predefined ones, or by adding new sets for sp ecial applications. Depending on the currently used finite element spaces, all degrees of freedom are automatically managed during mesh modifications.