The adaptive solution of partial differential equations by finite elements must be supported by suitable data structures. Besides an overview of existing adaptive mesh techniques, our analysis provides an abstract treatment discussing the necessary functionality independent of concrete representations. The different aspects can be organized in topological, geometric and the algebraic components.
Further considerations are necessary to support self-adaptivity in a multilevel context.
We distinguish between element based and node based data structures and will discuss their implementation in an object oriented language. Contributed September 15, 1992.