Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms

Abstract

A weak Galerkin finite element method is proposed for solving singularly perturbed problems with two parameters. A robust uniform optimal convergence has been proved in the corresponding energy and a stronger balanced norms using piecewise higher order discontinuous polynomials on a piecewise uniform Shishkin mesh. Finally, we give some numerical experiments to support theoretical results.