期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2009
卷号：2009
DOI：10.1155/2009/345196
出版社：Hindawi Publishing Corporation
摘要：We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on 𝑄=Ω×(0,𝑇], where Ω is a bounded domain in ℛ𝑑(𝑑≤4) with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in 𝑊1,𝑝(Ω) and 𝐿𝑝(𝑄) with 2≤𝑝<∞ and the almost two order superconvergence in 𝑊1,∞(Ω) and 𝐿∞(𝑄). Results of the 𝑝=∞ case are also included in two space dimensions (𝑑=1 or 2). By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.
