Mathematics > Numerical Analysis
[Submitted on 15 Sep 2021 (v1), last revised 22 Jul 2022 (this version, v2)]
Title:A local energy-based discontinuous Galerkin method for fourth order semilinear wave equations
View PDFAbstract:This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrite the problem into a system with a second-order spatial derivative, then apply the energy-based discontinuous Galerkin method to the system. The proposed scheme, on the one hand, is more computationally efficient compared with the local discontinuous Galerkin method because of fewer auxiliary variables. On the other hand, it is unconditionally stable without adding any penalty terms, and admits optimal convergence in the $L^2$ norm for both solution and auxiliary variables. In addition, the energy-dissipating or energy-conserving property of the scheme follows from simple, mesh-independent choices of the interelement fluxes. We also present a stability and convergence analysis along with numerical experiments to demonstrate optimal convergence for certain choices of the interelement fluxes.
Submission history
From: Lu Zhang [view email][v1] Wed, 15 Sep 2021 00:44:32 UTC (1,228 KB)
[v2] Fri, 22 Jul 2022 16:30:56 UTC (15,061 KB)
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