Adv. Appl. Math. Mech., 10 (2018), pp. 468-484.
Published online: 2018-10
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In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrödinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in $H^1$-norm with order $\mathcal{O}(h^2)$ between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in $H^1$-norm with order $\mathcal{O}(h^2)$ by the interpolation post-processing operator.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0156}, url = {http://global-sci.org/intro/article_detail/aamm/12221.html} }In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrödinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in $H^1$-norm with order $\mathcal{O}(h^2)$ between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in $H^1$-norm with order $\mathcal{O}(h^2)$ by the interpolation post-processing operator.