@Article{AAMM-15-1,
author = {Li, Di and Min, Liu and Xiliang, Lu and Zhijian, Yang, Jerry},
title = {The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {1},
pages = {30--48},
abstract = {<p style="text-align: justify;">This paper develops and analyzes interior penalty discontinuous Galerkin
(IPDG) method by patch reconstruction technique for Helmholtz problems. The technique achieves high order approximation by locally solving a discrete least-squares
over a neighboring element patch. We prove a prior error estimates in the $L^2$ norm
and energy norm. For each fixed wave number $k,$ the accuracy and efficiency of the
method up to order five with high-order polynomials. Numerical examples are carried
out to validate the theoretical results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0008},
url = {https://global-sci.com/article/72823/the-discontinuous-galerkin-method-by-patch-reconstruction-for-helmholtz-problems}
}