Uniform convergence and superconvergence of mixed finite element methods on anisotropically refined grids

The lowest order Raviart-Thomas rectangular element is considered for solvi ng the singular perturbation problem -div(a del p) + bp = f, where the diag onal tensor a = (epsilon(2), 1) or a = (epsilon(2), epsilon(2)). Global uni form convergence rates of O(N-1) for both p and a(1/2)del p in the L-2-norm are obtained in both cases, where N is the number of intervals in either d irection. The pointwise interior (away from the boundary layers) convergenc e rates of O(N-1) for p are also proved. Superconvergence (i.e., O(N-2)) at special points and O(N-2) global L-2 estimate for both p and a(1/2)del p a re obtained by a local postprocessing. Numerical results support our theore tical analysis. Moreover, numerical experiments show that an anisotropic me sh gives more accurate results than the standard global uniform mesh.