In this paper a combination of discontinuous, piecewise linear, finite elements with 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.

Finite difference methods (msc 65M06), Stability and convergence of numerical methods (msc 65M12), Method of lines (msc 65M20)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Hundsdorfer, W, & Jaffré, J. (2000). Implicit-explicit time stepping with spatial discontinuous finite elements. Modelling, Analysis and Simulation [MAS]. CWI.