A note on the application of the Guermond-Pasquetti mass lumping correction technique for convection-diffusion problems

TL;DR

This paper analyzes the Guermond-Pasquetti mass lumping correction technique for convection-diffusion problems, revealing how correction number affects accuracy differently for pure transport and diffusion cases.

Contribution

It provides a Fourier analysis of the correction technique, showing how increasing corrections impacts accuracy in transport and diffusion problems.

Findings

More corrections decrease accuracy in diffusion problems but improve it over the Galerkin scheme.

In transport problems, more corrections bring solutions closer to the consistent solution.

Corrected schemes outperform the Galerkin formulation in diffusion cases.

Abstract

We provide a careful Fourier analysis of the Guermond-Pasquetti mass lumping correction technique [Guermond J.-L., Pasquetti R. A correction technique for the dispersive effects of mass lumping for transport problems. - Computer Methods in Applied Mechanics and Engineering. - 2013. - Vol. 253. - P. 186-198] applied to pure transport and convection-diffusion problems. In particular, it is found that increasing the number of corrections reduces the accuracy for problems with diffusion; however all the corrected schemes are more accurate than the consistent Galerkin formulation in this case. For the pure transport problems the situation is the opposite. We also investigate the differences between two numerical solutions - the consistent solution and the corrected ones, and show that increasing the number of corrections makes solutions of the corrected schemes closer to the consistent solution in all cases.