A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations (Communications in Computational Physics, 2020)
The Douglas-Rachford and Peaceman-Rachford splitting methods are commonchoices for temporal discretizations of evolution equations. In this paper we combinethese methods with spatial discretizations fulfilling some easily verifiable criteria.In the setting of linear dissipative evolution equations we prove optimal convergenceorders, simultaneously in time and space. We apply our abstract results to dimensionsplitting of a 2D diffusion problem, where a finite element method is used for spatialdiscretization. To conclude, the convergence results are illustrated with numericalexperiments.