From the abstract: This thesis develops estimation techniques for the global error that occurs during the approximation of solutions of initial value problems on given intervals by multistep integration methods based on backward differentiation formulas (BDF). To this end, discrete adjoints obtained by adjoint internal numerical differentiation of the nominal integration scheme are used. For this purpose, a bridge between BDF methods and Petrov-Galerkin finite element methods is built by a novel functional-analytic framework. Goal-oriented global error estimators are derived in analogy to the dual weighted residual methodology in Galerkin methods for partial differential equations. Their asymptotic behavior, their accuracy in BDF methods with variable order and stepsize as well as their applicability for global error control are investigated.