• DOpElib (Differential Equations and Optimization Environment library) is a toolbox providing modularized highlevel algorithms mainly based on the deal.II Finite Element Library. (Supported versions are currently 9.0.1 until 9.5.3)
  • This enables researchers to implement only those moduls that are specific to their problem while being able to reuse other modules without further work.
  • The modularized access to the algorithms allows to switch between different algorithms for the same problem with little effort.
  • Software toolkit to solve – stationary and non- stationary – PDE problems as well as optimal control problems constrained by PDEs.


  • User needs to provide only the problem specific data, like element integrals and can use predefined modules for the solution of stationary and nonstationary PDEs in 1d, 2d, and 3d using a line-search Newton algorithm.
  • Various time stepping schemes (based on finite differences), such as forward Euler, backward Euler, Crank-Nicolson, shifted Crank-Nicolson, and Fractional-Step-Θ scheme.
  • Solution of optimization problems with PDE constraints with built in line search and trust region newton algorithms. In addition an interface to IPOPT and SNOPT is provided.
  • Different spatial triangulations for control and state variables.
  • All finite elements from deal.II including hp-support.
  • Mesh adaptation and goal-oriented error estimation.
  • Extensive source code and pdf documentations.


  • 43 examples (status July 2021) to demonstrate the capabilities of the library.
  • Many examples showing the solution of various PDEs including Poisson, Elasticity, Plasticity, Navier-Stokes, Fluid-Structure Interaction, and Phase-Field Fracture problems.
  • Several examples showing how to solve various kinds of optimization problems involving stationary and nonstationary PDE constraints.