Pointwise convergence of approximations to a convection–diffusion equation on a Shishkin mesh Original Research Article

A centered difference or finite element discretization is applied to a singularly perturbed, one-dimensional boundary value problem. The discretization uses a piecewise equidistant mesh. It is proved that the pointwise error is (almost) of second order with respect to the number of nodes, uniformly in the perturbation parameter. The proof is based on a monotonicity argument.