  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 ODE. However, Strang splitting suffers from order
reduction which limits its efficiency. This 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. Numerical examples including
a coupled mechanical system illustrate the proven convergence results.
