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In the numerical solution of partial differential equations (PDEs), a centralquestion is the one of building variational formulations that are inf-supstable not only at the infinite-dimensional level, but also at thefinite-dimensional one. This guarantees that residuals can be used to tightlybound errors from below and above and is crucial for a posteriori error controland the development of adaptive strategies. In this framework, the so-calledDiscontinuous Petrov--Galerkin (DPG) concept can be viewed as a systematicstrategy of contriving variational formulations which possess these desirablestability properties, see e. g. Broersen et al. [2015]. In this paper, wepresent a C++ library, Dune-DPG, which serves to implement and solve suchvariational formulations. The library is built upon the multipurpose finiteelement package Dune (see Blatt et al. [2016]). One of the main features ofDune-DPG is its flexibility which is achieved by a highly modular structure.The library can solve in practice some important classes of PDEs (whose rangegoes beyond classical second order elliptic problems and includes e. g.transport dominated problems). As a result, Dune-DPG can also be used toaddress other problems like optimal control with the DPG approach.

The DUNE-DPG library for solving PDEs with Discontinuous Petrov--Galerkin finite elements