An energy-based discontinuous Galerkin method for wave equations on complex geometric domains
Abstract
This paper develops a high-order cut energy-based discontinuous Galerkin (CutEDG) method for second-order acoustic wave equations on complex domains and across stationary material interfaces. The method employs unfitted Carte- sian meshes and addresses the small-cut-cell problem by introducing ghost-penalty stabilization directly into the local bilinear forms defining the EDG energy, while leaving the original spatial coupling and numerical-flux structure unchanged. We establish semidiscrete energy stability and a priori error estimates showing that high-order accuracy is retained. The formulation is further extended to interface problems with discontinuous wave speeds. Numerical experiments confirm the pre- dicted convergence rates and demonstrate robustness with respect to arbitrarily small cut cells. In particular, the explicit time-step restriction is governed by the background mesh size rather than the smallest physical cut cell, and the stabilized energy Gram matrices exhibit cut-independent conditioning.
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BibTeX
@misc{fu2026energybased,
title = {{An energy-based discontinuous Galerkin method for wave equations on complex geometric domains}},
author = {Yangxin Fu and Yan Jiang and Siyang Wang and Lu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38378},
eprint = {2609.38378},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38378},
}
RIS
TY - UNPB
TI - An energy-based discontinuous Galerkin method for wave equations on complex geometric domains
AU - Yangxin Fu
AU - Yan Jiang
AU - Siyang Wang
AU - Lu Zhang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38378
UR - https://arxiv.org/abs/2609.38378
AB - This paper develops a high-order cut energy-based discontinuous Galerkin (CutEDG) method for second-order acoustic wave equations on complex domains and across stationary material interfaces. The method employs unfitted Carte- sian meshes and addresses the small-cut-cell problem by introducing ghost-penalty stabilization directly into the local bilinear forms defining the EDG energy, while leaving the original spatial coupling and numerical-flux structure unchanged. We establish semidiscrete energy stability and a priori error estimates showing that high-order accuracy is retained. The formulation is further extended to interface problems with discontinuous wave speeds. Numerical experiments confirm the pre- dicted convergence rates and demonstrate robustness with respect to arbitrarily small cut cells. In particular, the explicit time-step restriction is governed by the background mesh size rather than the smallest physical cut cell, and the stabilized energy Gram matrices exhibit cut-independent conditioning.
ER -