Fourier analysis of semi-discrete and space–time stabilized methods for the advective–diffusive–reactive equation: III. SGS/GSGS Original Research Article

In this paper, the work initiated in part one and two is extended to the transient subgrid scale/gradient subgrid scale (SGS/GSGS) stabilized method. Temporal accuracy and stability of semi-discrete and time-discontinuous space–time versions of the method are examined for transient advection–diffusion–reaction problems. Also, for the above methods, predictor multi-corrector algorithms are analyzed, with special emphasis on mass and source lumping, which has been shown to enhance both, stability and accuracy of “explicit” stabilized methods. It will be shown that the parent SUPG, SGS and SGS/GSGS methods perform very similarly, and that explicit predictor multi-corrector mass–source lumping practically retains the accuracy of the parent method, while gaining stability.