A high-order space-time ultra-weak discontinuous Galerkin method for the second-order wave equation in one space dimension

被引：18

作者：

Baccouch, Mahboub ^{[1
]}

Temimi, Helmi ^{[2
]}

机构：

[1] Univ Nebraska, Dept Math, Omaha, NE 68182 USA

[2] Gulf Univ Sci & Technol, Dept Math & Nat Sci, POB 7207, Hawally 32093, Kuwait

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 389卷

关键词：

Ultra-weak Discontinuous Galerkin method; Second-order wave equation; Space-time scheme; Convergence; A priori error estimation; FINITE-ELEMENT-METHOD; CONSERVATION-LAWS; SUPERCONVERGENCE;

D O I：

10.1016/j.cam.2020.113331

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：20

共 50 条

[31] A high-order space-time spectral method for the distributed-order time-fractional telegraph equation
Derakhshan, M. H.
Kumar, Pushpendra
Salahshour, Soheil
[J]. INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL, 2024, 12 (08) : 2778 - 2794
[32] Time and space adaptivity of the wave equation discretized in time by a second-order scheme
Gorynina, Olga
Lozinski, Alexei
Picasso, Marco
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2019, 39 (04) : 1672 - 1705
[33] High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation
Min Zhang
Yang Liu
Hong Li
[J]. Communications on Applied Mathematics and Computation, 2020, 2 : 613 - 640
[34] High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation
Zhang, Min
Liu, Yang
Li, Hong
[J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2020, 2 (04) : 613 - 640
[35] Extension of the High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme to Solve Time Dependent Diffusion Equations
Tu, Shuangzhang
Skelton, Gordon W.
Pang, Qing
[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 11 (05) : 1503 - 1524
[36] High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension
Baruch, G.
Fibich, G.
Tsynkov, S.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (01) : 820 - 850
[37] HIGH ORDER CUT DISCONTINUOUS GALERKIN METHODS FOR HYPERBOLIC CONSERVATION LAWS IN ONE SPACE DIMENSION
Fu, Pei
Kreiss, Gunilla
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2021, 43 (04): : A2404 - A2424
[38] Residual-based a posteriori error analysis of an ultra-weak discontinuous Galerkin method for nonlinear second-order initial-value problems
Baccouch, Mahboub
[J]. NUMERICAL ALGORITHMS, 2024,
[39] Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method
van Zwieten, J. S. B.
Sanderse, B.
Hendrix, M. H. W.
Vuik, C.
Henkes, R. A. W. M.
[J]. COMPUTERS & FLUIDS, 2017, 156 : 34 - 47
[40] Solution of space-time tempered fractional diffusion-wave equation using a high-order numerical method
Saffarian, Marziyeh
Mohebbi, Akbar
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 423

← 1 2 3 4 5 →