ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements

A Cangiani, Z Dong, E Georgoulis - Mathematics of Computation, 2022 - ams.org
We extend the applicability of the popular interior penalty discontinuous Galerkin method
discretizing advection-diffusion-reaction problems to meshes comprising extremely general …

Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes

R Li, Y Gao, Z Chen - Numerical Algorithms, 2024 - Springer
In this paper, we develop a polygonal mesh adaptation algorithm for a fully implicit scheme
based on discontinuous Galerkin (DG) finite element methods in space and backward Euler …

A Stokes–Darcy–Darcy model and its discontinuous Galerkin method on polytopic grids

R Li, Y Gao, CS Zhang, Z Chen - Journal of Computational Physics, 2024 - Elsevier
In this paper, we propose and numerically solve a model considering confined flow in
fractured porous media coupled with free flow in conduits. Such a situation arises, for …

Quadrature-free polytopic discontinuous Galerkin methods for transport problems

TJ Radley, P Houston, ME Hubbard - arXiv preprint arXiv:2310.10406, 2023 - arxiv.org
In this article we consider the application of Euler's homogeneous function theorem together
with Stokes' theorem to exactly integrate families of polynomial spaces over general …

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems

EN Karatzas - arXiv preprint arXiv:2301.12577, 2023 - arxiv.org
In the present work, we examine and analyze an hp-version interior penalty discontinuous
Galerkin finite element method for the numerical approximation of a steady fluid system on …