An object-oriented approach for parallel two- and three-dimensional adaptive finite element computations

For the mathematically sound, cost effective, flexible and automatic computation of structural mechanical problems with error tolerances, adaptive finite element meshes (h-adaptivity) and elements with different Ansatz order (p-adaptivity) and dimension (d-adaptivity) are desirable. Furthermore, because of the numerical effort, the use of parallel computers is adequate. Object-oriented data structures and algorithms are presented which support these adaptive formulations. In this paper, we describe a refinement algorithm which adapts hexahedral meshes in a node regular way, i.e. without hanging nodes. Moreover, classes implementing the mathematical operators and structures arising in the finite element formulation are introduced within the object oriented concept. They offer the means to implement FE formulations in a way, very similar to the mathematical notation. For these purposes, an object-oriented language is strongly required in order to get a general and simple program structure, even for highly complex tasks with h-, p- and d-adaptivity and distributed data.