A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes

TL;DR

This paper introduces a numerical algorithm that effectively solves the Hemker problem by using asymptotic-informed Shishkin meshes and multiple coordinate systems, demonstrating its efficiency through numerical results.

Contribution

The paper presents a novel numerical algorithm that incorporates asymptotic analysis and multiple coordinate systems for solving the Hemker problem with improved accuracy.

Findings

Effective solution of Hemker problem demonstrated

Use of asymptotic information improves mesh design

Numerical results confirm algorithm's efficiency

Abstract

A numerical algorithm is presented to solve a benchmark problem proposed by Hemker. The algorithm incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due to the different geometries and associated layer structures that are involved in this problem. Numerical results are presented to demonstrate the effectiveness of the proposed numerical algorithm.