Mao, Fengmei; Zhang, Houchao A Hermite-type rectangular mixed finite element analysis for four order nonlinear dispersion-dissipative wave equations. (Chinese. English summary) Zbl 1363.65169 Math. Pract. Theory 46, No. 2, 262-269 (2016). 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 Keywords:fourth order nonlinear wave equations; strong damping; Hermite-type rectangular element; semi-discrete scheme; full-discrete scheme; finite element method; error estimate; Ritz projection; superconvergence PDFBibTeX XMLCite \textit{F. Mao} and \textit{H. Zhang}, Math. Pract. Theory 46, No. 2, 262--269 (2016; Zbl 1363.65169)