A higher order finite element method with modified graded mesh for singularly perturbed two‐parameter problems

Abstract

This paper presents a modified graded mesh for singularly perturbed two‐parameter problems. The mesh is generated recursively using Newton's algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on higher order polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ε‐weighted energy norm. A test example is taken to compare the proposed graded mesh with others found in the literature.