Shishkin mesh simulation: A new stabilization technique for convection-diffusion problems and complementary experiments

TL;DR

This paper discusses the Shiskin mesh simulation (SMS), a new stabilization technique for convection-diffusion problems, along with complementary experiments to evaluate its performance, emphasizing reproducibility and practical implementation.

Contribution

It introduces the SMS method for stabilization in convection-diffusion problems and provides additional experimental data to support its effectiveness.

Findings

SMS improves stability in convection-diffusion simulations

Source codes are available for reproducibility

Complementary experiments validate the method's performance

Abstract

We present together in this document the paper B. Garc\'ia-Archilla, Shiskin mesh simulation: A new stabilization technique for convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 256 (2013), 1-16, and the manuscript B. Garc\'{\i}a-Archilla, Shiskin mesh simulation: Complementary experiments, which contains some of the experiments that, for the sake of brevity were not included in the first one. This second paper with complementary experiments is neither self-contained nor intended to be published in any major journal, but is intended to be accessible to anyone wishing to learn more on theperformance of the SMS method. Following a principle of reproducible computational research, the source codes of the experiments in the present papers are available from the author on request or on "http://personal.us.es/bga/bga_files/software_bga.html". Excluded are the codes corresponding to Example 7 which is subject of current resarch