Shi, Dongyang; Guo, Cheng; Wang, Haihong A nonconforming \(H^1\)-Galerkin expanded mixed finite element method for semilinear parabolic partial differential equations. (Chinese. English summary) Zbl 1289.65227 Chin. J. Eng. Math. 30, No. 2, 252-262 (2013). Summary: The parabolic partial differential equations have a wide range of applications in the heat transmission, the solute dissemination, porous media seepage and so on. In this paper, a nonconforming Galerkin expanded finite element method for a class of quasi-linear partial differential equations is proposed both for semi-discrete and back-ward Euler full discrete schemes by applying the advantages of Galerkin mixed finite element method and expanded finite element method. The same error estimates as the conforming case in the previous literature, the existence and the uniqueness of the finite element solutions and the stability of the schemes are obtained by means of the interpolation of the true solutions instead of projections. 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 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35K58 Semilinear parabolic equations 35K59 Quasilinear parabolic equations Keywords:\(H^1\)-Galerkin expanded mixed finite element method; nonconforming finite element; quasilinear parabolic partial differential equation; semi-discrete and fully discrete scheme; error estimates; semilinear parabolic partial differential equations; stability PDFBibTeX XMLCite \textit{D. Shi} et al., Chin. J. Eng. Math. 30, No. 2, 252--262 (2013; Zbl 1289.65227)