Splitting methods for constrained diffusion-reaction systems

We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure seems promising as we can treat the nonlinearity separately. This has some computational advantages, since we only have to solve a linear constrained system and a nonlinear ordinary differential equation. However, Strang splitting suffers from order reduction which limits its efficiency. This reduction is caused by the fact that the nonlinear subsystem produces inconsistent initial values for the constrained subsystem. The incorporation of an additional correction term resolves this problem without increasing the computational cost significantly. Numerical examples including a coupled mechanical system illustrate the proved convergence results.