Local Error Estimates for the SUPG Method Applied to Evolutionary Convection–Reaction–Diffusion Equations

Abstract

Local error estimates for the SUPG method applied to evolutionary convection---reaction---diffusion equations are considered. The steady case is reviewed and local error bounds are obtained for general order finite element methods. For the evolutionary problem, local bounds are obtained when the SUPG method is combined with the backward Euler scheme. The arguments used in the proof lead to estimates for the stabilization parameter that depend on the length on the time step. The numerical experiments show that local bounds seem to hold true both with a stabilization parameter depending only on the spatial mesh grid and with other time integrators.