Uniformly superconvergent analysis of an efficient two-grid method for nonlinear Bi-wave singular perturbation problem

Abstract The main aim of this paper is to present a two-grid method for the fourth order nonlinear Bi-wave singular perturbation problem with low order nonconforming finite element based on the Ciarlet–Raviart scheme. The existence and uniqueness of the approximation solution are demonstrated through the Brouwer fixed point theorem and the uniform superconvergent estimates in the broken H 1 − norm and L 2 − norm are obtained, which are independent of the perturbation parameter δ. Some numerical results indicate that the proposed method is indeed an efficient algorithm.

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