Object oriented finite element calculations using maple

Modern Computer Algebra Systems (CAS), such as Maple or Mathematica, with their symbolic facilities and visualization possibilities are powerful tools to design data structures and algorithms used in numerical simulation, with significantly lower costs compared to straightforward implementation in ''real'' programming languages, such as, for example, C or Java. The present paper shows how the CAS Maple can be used to design finite element software using linear and hierarchical bases. As a computational example the two-dimensional Poisson-equation with Dirichlet boundary conditions is presented.