Non-Symmetric Interior Penalty Galerkin Finite Element Method for a Class of Singularly Perturbed Reaction Diffusion Problems with Discontinuous Data

This paper presents a non-symmetric interior penalty Galerkin finite element method for a class of one dimensional singularly perturbed reaction–diffusion problems with discontinuous coefficients. The solution of this class of problem has been observed to exhibit boundary and interior layers. The error estimates in the energy as well as the balanced norm have been derived. It has been observed that errors are uniform with respect to the perturbation parameter ε. The numerical solution of the problem has been computed using the method proposed in the study to support the corresponding theoretical results. The uniformness of the error estimates with respect to the perturbation parameter ε has been established numerically for the L∞-norm. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.