Estimations of the discrete Green's function of the SDFEM on Shishkin triangular meshes for problems with only exponential layers

TL;DR

This paper provides estimations of the discrete Green's function for the SDFEM on Shishkin meshes, specifically targeting problems with exponential layers, to improve understanding of numerical stability and accuracy.

Contribution

It introduces new estimations of the discrete Green's function for SDFEM on Shishkin meshes, addressing problems with exponential layers.

Findings

Derived bounds for the Green's function on Shishkin meshes

Enhanced understanding of SDFEM stability in exponential layer problems

Potential improvements in numerical solution accuracy

Abstract

In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for problems with only exponential layers.