A super-convergent quasi-discontinuous Galerkin method for advection-diffusion problems
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.
Related
- A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems
- A Discontinuous Galerkin Method for Biharmonic Dirichlet Control Problems With Patch Reconstruction
- A Fully Discrete Local Discontinuous Galerkin Method for Quasilinear Stochastic Convection-Diffusion-Type Equations
- Transport-Matched Penalties for Diffusion Synthetic Acceleration of Polytopic Discontinuous Galerkin Discretisations
- A weighted polygonal discontinuous Galerkin method for hierarchically coupled reaction-diffusion systems with cubic interactions
BibTeX
@misc{roux2026superconvergent,
title = {{A super-convergent quasi-discontinuous Galerkin method for advection-diffusion problems}},
author = {Daniel Y Le Roux},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29818},
eprint = {2610.29818},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05775566v1},
}
RIS
TY - UNPB
TI - A super-convergent quasi-discontinuous Galerkin method for advection-diffusion problems
AU - Daniel Y Le Roux
PY - 2026
DA - 2026/10/20
PB - HAL
DO - 10.48550/arxiv.2610.29818
UR - https://hal.science/hal-05775566v1
AB - 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.
ER -