Variational Methods for Stable Time Discretization of First-Order Differential Equations

Abstract

Starting from the well-known discontinuous Galerkin (dG) and continuous Galerkin-Petrov (cGP) time discretization schemes we derive a general class of variational time discretization methods providing the possibility for higher regularity of the numerical solutions. We show that the constructed methods have the same stability properties as dG or cGP, respectively, making them well-suited for the discretization of stiff systems of differential equations. Additionally, we empirically investigate the order of convergence and performance depending on the chosen method.