Convergence and Supercloseness in a Balanced Norm of Finite Element Methods on Bakhvalov-Type Meshes for Reaction-Diffusion Problems

In convergence analysis of finite element methods for singularly perturbed reaction–diffusion problems, balanced norms have been successfully introduced to replace standard energy so that layers can be captured. this article, we focus on the in a norm Bakhvalov-type rectangular meshes. order achieve our goal, novel interpolation operator, which consists local $$L^2$$ projection operator and Lagrange is optimal norm. The also depends stabilities characteristics Furthermore, obtain supercloseness result norm, appears literature first time. This another interpolant, vertices-edges-element some corrections boundary.