Mao, Fengmei; Diao, Qun; Wang, Junjun A new superconvergence analysis and extrapolation of Hermite-type finite element for nonlinear pseudo-hyperbolic equations. (Chinese. English summary) Zbl 1340.65224 J. Zhengzhou Univ., Nat. Sci. Ed. 47, No. 1, 6-9, 23 (2015). Summary: A Hermit-type rectangular element approximation is discussed for a class of nonlinear pseudo-hyperbolic equations under semi-discrete scheme. The superclose properties and the global superconvergence with order \(O(h^3)\) for the exact \(u\) in \(H^1\) norm are obtained through interpolated post-processing approach. Furthermore, by constructing a suitable auxiliary problem, the extrapolation solution with order \(O(h^4)\) is deduced through the Richardson scheme. MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35L82 Pseudohyperbolic equations Keywords:nonlinear pseudo-hyperbolic equation; Hermite-type rectangular element; superconvergence; extrapolation; semidiscretization; Richardson scheme PDFBibTeX XMLCite \textit{F. Mao} et al., J. Zhengzhou Univ., Nat. Sci. Ed. 47, No. 1, 6--9, 23 (2015; Zbl 1340.65224) Full Text: DOI