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Superconvergence analysis of a new nonconforming mixed finite element approximation for second order hyperbolic equation. (Chinese. English summary) Zbl 1374.65151

Summary: A new nonconforming mixed finite element method for second order hyperbolic equation is studied based on a new mixed variational form. By utilizing the properties of the interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time \(t\) instead of the Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the superclose properties and the global superconvergence with order \(O(h^2)\) for the primitive solution \(u\) in broken \(H^1\)-norm and the flux \(\vec{p}=-\nabla u\) in \(L^2\)-norm are obtained through interpolated postprocessing approach, respectively. Furthermore, some numerical example results are provided to show the validity of the theoretical analysis.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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