Abstract Roos and Stynes Some open questions in the numerical analysis of singularly perturbed differential equations, Comput. Methods Appl. Math. 15 2015, 4, 531–550 posed several open problems, one of which is obtaining uniform convergence of higher-order finite element methods on Bakhvalov-type meshes. In this article, we propose a finite element analysis of any order on an eXp-Bakhvalov mesh to solve a two-dimensional singularly perturbed boundary value problem, whose solution exhibits exponential layers. A careful selection of the interpolation operator, considering the characteristics of the layers, allows the finite element method to achieve optimal-order convergence with respect to the singular perturbation parameter. Numerical results are presented to support the theoretical findings.
Sahu et al. (Thu,) studied this question.