A non standard fitted operator robust method for 2D singularly perturbed elliptic convection-diffusion problems with general shift arguments

Purpose The purpose of this work is to develop and analyze a robust numerical method without any constraints on the mesh size for 2D singularly perturbed elliptic convection-diffusion problems with general shift arguments. Design/methodology/approach In the development of a numerical method for the considered problem, we used the non standard fitted operator method based on Micken's techniques. An interpolation technique is incorporated into the proposed method to effectively handle the shift terms. Findings The significant improvement of this work compared to previous research is its ability to deal with shifts of both small and large values without any constraints on the mesh size. A rigorous analysis is carried out to obtain the consistency and stability of the numerical method. The proposed numerical method is parameter-uniform convergent with optimal order. Numerical experiments have been performed to corroborate the proposed theoretical results. The effects of shifts on solution behavior have been demonstrated through tables and figures. Originality/value The novelty of the present work is to introduce a robust numerical method for the considered class of problems and overcome the limitations of existing methods. Numerical results obtained from the proposed method have been compared with existing methods in the literature.