Concepts for Object-Oriented Finite Element Software – the deal.II Library

An overview of the deal.II library is given. This library provides the functionality needed by modern numerical software used in the finite element solution of partial differential equations, offering adaptively refined meshes, different finite element classes, multigrid solvers and support for one, two and three spatial dimensions. We give a description of the basic design criteria used in the development of the library and how they were transformed into actual code, and some examples of the use of the library in numerical analysis. 1 Design and evolution of deal.II The DEAL project, short for Differential Equations Analysis Library, was started to provide means for the implementation of adaptive finite element methods. In fact, the development of DEAL and adaptive methods at the Institute of Applied Mathematics in Heidelberg are closely linked. From this starting point, a finite element library was needed, that is able to handle grids with strongly varying mesh width and supports strategies for the computation of error estimates based on dual problems. While DEAL was a library developed since 1993, this article gives an overview of the design criteria, programming models and fields of application of its successor library, deal.II.