Error analysis for a spectral element method for solving two-parameter singularly perturbed diffusion equation

Abstract

In this paper, we study the two-parameter spectral element method based on weighted shifted orthogonal polynomials for solving singularly perturbed diffusion equation on an interval [0, 1] which are modeled with singular parameters. We continue our study to estimate the lower bound of the weighted orthogonal polynomial coefficient and the upper bound of a posteriori error estimates of the method through different weighted norms to minimize the computational cost. Numerical examples are implemented to study the applicability and efficiency of the technique. The obtained error bounds for the coefficient of orthogonal polynomials and the posteriori estimates fall within the bounds derived in the theoretical section. It is also observed that the two weighted norms decreases when the values of [Formula: see text] and [Formula: see text] increases for the three choices of [Formula: see text] and for different values of x and y. The quality and accuracy of the solution can be realized through figures and tables.