## A new superconvergence analysis and extrapolation of Hermite-type finite element for nonlinear pseudo-hyperbolic equations.(Chinese. English summary)Zbl 1340.65224

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
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