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arXiv · 2610.29818

A Super-Convergent Quasi-Discontinuous Galerkin Method for Advection-Diffusion Problems

Daniel Y Le Roux
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Abstract

The aim of the present study is to develop discontinuous Galerkin and nonconforming finite-element methods for solving the 2D advection-diffusion equation. The discrete formulations are stabilized by means of a family of numerical fluxes and the dispersion relations are constructed via a Fourier/stability analysis. The linear discontinuous P1DG and non conforming P1NC Galerkin discretizations are studied. A long time stability result is proven for the P1NC and P1DG schemes and fluxes examined here by inspecting the discrete frequencies, solutions of the dispersion relations. A super-convergent result is also demonstrated for the P1NC discrete frequency (O(h 4 ) accuracy) compared to the P1DG one (O(h 2 ) accuracy). These results are in line with those obtained in a previous paper for the shallow-water system.

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BibTeXRIS

Daniel Y Le Roux. 2026-10-21. A Super-Convergent Quasi-Discontinuous Galerkin Method for Advection-Diffusion Problems. https://arxiv.org/abs/2610.29818

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