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On A System For Adaptive, Parallel Finite Element Computations

The principal aspects are outlined of a prototype, adaptive finite element system for the solution of a class of linear, elliptic problems defined by a weak mathematical formulation. The system uses results about computable a-posteriori estimates and asymptotically optimal meshes developed earlier by the authors to control the adaptive mesh refinement and to provide an optimal solution within a prescribed cost range. Moreover, the system takes advantage of natural parallelism and modularity of the method. An overview of the principal error estimation results is presented, the overall systems design is outlined, and a data structure for the mesh refinement, based on a novel tree structure, is discussed. Some numerical results obtained with a preliminary version of the system illustrate the effectivity of the approach.