TY - JOUR
T1 - A high-order space–time ultra-weak discontinuous Galerkin method for the second-order wave equation in one space dimension
AU - Baccouch, Mahboub
AU - Temimi, Helmi
N1 - Funding Information:
This research was partially supported by the Kuwait Foundation for the Advancement of Sciences (Project Code: PR17-16SM-04 ). Also the first author was partially supported by the NASA Nebraska Space Grant, USA (Federal Grant/Award Number 80NSSC20M0112 ). The author would like to thank the two anonymous reviewers for the valuable comments and suggestions which improved the quality of the paper.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/6
Y1 - 2021/6
N2 - In this paper, we present and analyze a new space–time ultra-weak discontinuous Galerkin (UWDG) finite element method for the second-order wave equation in one space dimension. The UWDG finite element approximations are used in space variable and also for the temporal approximation. The space–time UWDG discretization is presented in detail, including the definition of the numerical fluxes, which are necessary to obtain optimal error estimates. The proposed scheme can be made arbitrarily high-order accurate in both space and time. The error estimates of the presented semi-discrete and fully-discrete schemes are both analyzed. Several numerical examples are provided to confirm the theoretical results.
AB - In this paper, we present and analyze a new space–time ultra-weak discontinuous Galerkin (UWDG) finite element method for the second-order wave equation in one space dimension. The UWDG finite element approximations are used in space variable and also for the temporal approximation. The space–time UWDG discretization is presented in detail, including the definition of the numerical fluxes, which are necessary to obtain optimal error estimates. The proposed scheme can be made arbitrarily high-order accurate in both space and time. The error estimates of the presented semi-discrete and fully-discrete schemes are both analyzed. Several numerical examples are provided to confirm the theoretical results.
KW - A priori error estimation
KW - Convergence
KW - Second-order wave equation
KW - Space–time scheme
KW - Ultra-weak Discontinuous Galerkin method
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U2 - 10.1016/j.cam.2020.113331
DO - 10.1016/j.cam.2020.113331
M3 - Article
AN - SCOPUS:85098563533
SN - 0377-0427
VL - 389
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 113331
ER -