Construction of Local Finite Element Spaces Using the Generic Reference Elements -- DUNE-FEM. A General Purpose Discretization Toolbox for Parallel and Adaptive Scientific Computing -- The DUNE-PRISMGRID Module -- Performance Pitfalls in the DUNE Grid Interface -- DUNE-MULTIDOMAINGRID: A Metagrid Approach to Subdomain Modeling -- A Software Framework for Reduced Basis Methods using DUNE-RB and RBMATLAB -- DUNE-UDG: A Cut-Cell Framework for Unfitted Discontinuous Galerkin Methods -- Solving Optimal Control Problems with the KASKADE 7 Finite Element Toolbox -- The DuMux Material Law Framework -- Using DUNE-PDELAB for Two-phase Flow in PorousMedia -- On the Implementation of a HeterogeneousMulti-scale Finite Element Method for Nonlinear Elliptic Problems -- On the Analysis of Porous Media Dynamics using a DUNE-PANDAS Interface -- An Implementation of Hybrid Discontinuous Galerkin Methods in DUNE.

DUNE, the Distributed and Unified Numerics Environment, is an open-source modular toolbox for solving partial differential equations with grid-based methods. This book covers recent advances in the development and usage of DUNE.  It consists of a collection of 13 articles which mainly evolved from talks  given at the First DUNE User Meeting in Stuttgart, Germany, 6.-8.10.2010. The articles nicely illustrate the advanced capabilities and the strong versatility of the DUNE framework. The first part presents extensions of the DUNE core modules, including the construction of local finite element spaces, a discretization toolbox, and two meta-grids, as well as a discussion of performance pitfalls. The second part introduces several external DUNE modules dealing with, e.g., reduced basis methods, unfitted discontinuous Galerkin methods, optimal control problems, and porous media applications. Specific methods and applications are subject of the third part, ranging from two-phase flow in porous media over the implementation of hybrid discontinuous Galerkin and heterogeneous multi-scale methods up to the coupling of DUNE with an existing finite element package.