TY - JOUR
T1 - The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems
AU - Li , Di
AU - Liu , Min
AU - Lu , Xiliang
AU - Yang , Jerry Zhijian
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 30
EP - 48
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2022-0008
UR - https://global-sci.org/intro/article_detail/aamm/21124.html
KW - Least-squares reconstruction, Helmholtz problems, patch reconstruction, discontinuous Galerkin, error estimates.
AB - <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>