A novel approach for solving the Landau-Lifshitz-Gilbert equation for antiferromagnets with the finite-element method is presented. The antiferromagnet is treated in a continuum theory which allows us to explore the domain structure on a mesoscopic length scale. The finite-element method is suitable to treat antiferromagnets with arbitrarily shaped grains as well as exchange coupled antiferromagnetic (AF)/ferromagnetic (F) structures. The change of the domain configuration in the antiferromagnet after the reversal of the ferromagnet leads to exchange bias in AF/F bilayers with perfectly compensated interfaces.