Robust hybrid schemes of higher order for singularly perturbed convection-diffusion problems

Abstract

Abstract A class of linear singularly perturbed convection-diffusion problems in one dimension is discretized on the Shishkin mesh using hybrid higher-order finite-difference schemes. Under appropriate conditions, pointwise convergence uniform in the perturbation parameter e is proved for one of the discretizations. This is done by the preconditioning approach, which enables the proof of e-uniform stability and e-uniform consistency, both in the maximum norm. The order of convergence is almost 3 when e is sufficiently small.