Superconvergence of an -Galerkin nonconforming mixed finite element method for a parabolic equation

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• 作者：Yadong Zhang ; Dongyang Shi
• 关键词：H1H1-Galerkin mixed FEM ; Superconvergence ; Nonconforming FE ; Parabolic problem ; Semi-discrete and fully-discrete schemes
• 刊名：Computers and Mathematics with Applications
• 出版年：December, 2013
• 年：2013
• 卷：66
• 期：11
• 页码：2362-2375
• 全文大小：553 K

文摘

By choosing a suitable pair of approximating spaces, an -Galerkin nonconforming mixed finite element method (FEM) is proposed for a class of parabolic equations under semi-discrete, backward Euler and Crank-Nicolson fully-discrete schemes, in which the famous element and zero order Raviart-Thomas element are used to approximate the primitive solution and the flux , respectively. Based on special characters of the elements considered, the corresponding optimal order error estimates for in broken -norm and in -norm are obtained for the above schemes. Furthermore, the global superconvergence results are derived through the postprocessing technique. The numerical results show the validity of the theoretical analysis.