Discontinuous Galerkin time stepping with local projection stabilization for transient convection–diffusion-reaction problems

A time-dependent convection–diffusion-reaction problem is discretized in space by a continuous finite element method with local projection stabilization and in time by a discontinuous Galerkin method. We present error estimates for the semidiscrete problem after discretizing in space only and for the fully discrete problem. Numerical tests confirm the theoretical results.