 Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite elementDongyang Shi and Junjun Wang Applied Mathematics and Computation, 2017, vol. 305, issue C, 1-16 Abstract: Nonlinear hyperbolic equation is studied by developing a linearized Galerkin finite element method (FEM) with nonconforming EQ1rot element. A time-discrete system is established to split the error into two parts which are called the temporal error and the spatial error, respectively. The temporal error is proved skillfully which leads to the analysis for the regularity of the time-discrete system. The spatial error is derived τ-independently with order O(h2+hτ) in broken H1-norm. The final unconditional superclose result of u with order O(h2+τ2) is deduced based on the above achievements. The two typical characters of this nonconforming EQ1rot element (see Lemma 1 below) play an important role in the procedure of proof. At last, a numerical example is provided to support the theoretical analysis. Here, h is the subdivision parameter, and τ, the time step. Keywords: Nonlinear hyperbolic equation; Nonconforming EQ1rot element; Linearized Galerkin FEM; Unconditional superclose estimate (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:305:y:2017:i:c:p:1-16 DOI: 10.1016/j.amc.2017.01.050 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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