Abstract
We discuss the superconvergence analysis of the Galerkin finite element method for the singularly perturbed coupled system of both reaction–diffusion and convection–diffusion types. The superconvergence study is carried out by using linear finite element, and it is shown to be second-order (up to a logarithmic factor) uniformly convergent in the suitable discrete energy norm. We have conducted some numerical experiments for the system of reaction–diffusion and system of convection–diffusion models, which validate the theoretical results.
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