Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case

We introduce a defect correction principle for exponential operator splitting methods applied to time-dependent linear Schrödinger equations and construct a posteriori local error estimators for the Lie-Trotter and Strang splitting methods. Under natural commutator bounds on the involved operators we prove asymptotical correctness of the local error estimators, and along the way recover the known a priori convergence bounds. Numerical examples illustrate the theoretical local and global error estimates