Implicit–explicit time stepping with spatial discontinuous finite elements Original Research Article

In this paper a combination of discontinuous, piecewise linear, finite elements with BDF2 implicit–explicit time stepping is considered for convection–reaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for one-dimensional problems. Furthermore, attention will be given to the stability and TVD properties of the explicit BDF2-type formula used for convection in the implicit–explicit time stepping.