A mixed discontinuous Galerkin method for the wave equation. (15th January 2021)

• Record Type: Journal Article
• Authors: He, Limin; Wang, Fei; Wen, Jing
• Is Part Of: Computers & mathematics with applications. Volume 82(2021)
• Page Start: 60
• Page End: 73
• Publication Date: 2021-01-15
• Subjects: Mixed discontinuous Galerkin method -- Spatially semi-discrete approximation -- Wave equation -- Optimal error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.12.001
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We study a mixed discontinuous Galerkin (DG) method for solving the second-order wave equation. The stress variable p and the displacement variable u are discretized by the mixed DG element pair P k + 1 – P k ( k ≥ 0 ). Under appropriate regularity assumptions on the solution pair, we derive optimal error estimates for the spatially semi-discrete scheme. Specifically, we prove the optimal convergence orders for u in L 2 norm and p in L 2 norm. Some test problems are presented, and the numerical results show that the orders of convergence coincide with the predicted error estimates.