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A Hermite-type rectangular mixed finite element analysis for four order nonlinear dispersion-dissipative wave equations. (Chinese. English summary) Zbl 1363.65169

Summary: A Hermite-type mixed finite element method is proposed for a class of fourth order strongly damped nonlinear wave equations. The existence and uniqueness are proved under semi-discrete scheme of solution. By use of integral identity result of element, an error estimate is established between the interpolation and Ritz projection, the superclose properties with order \(O(h^3)\) are derived for semi-discrete scheme. Then the global superconvergence is deduced by interpolation post-processing technique. Moreover, the superclose results with order \(O(h^3 + r)\) are obtained through constructing a new full-discrete 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
35L75 Higher-order nonlinear hyperbolic equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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