Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation

• Published in: Applied mathematics and computation Vol. 274; pp. 182 - 194
• Main Authors: Dongyang, Shi, Fengna, Yan, Junjun, Wang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2016
• Subjects: Mixed finite element method; Nonlinear Sobolev equation; Semi-discrete and fully-discrete schemes; τ-independent superclose and superconvergence results; 65N15; Mixed finite element method; Semi-discrete and fully-discrete schemes; Nonlinear Sobolev equation; 65N30; τ-independent superclose and superconvergence results
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2015.09.004

In this paper, a new mixed finite element scheme is proposed for the nonlinear Sobolev equation by employing the finite element pair Q11/Q01 × Q10. Based on the combination of interpolation and projection skill as well as the mean-value technique, the τ-independent superclose results of the original variable u in H1-norm and the variable q→=−(a(u)∇ut+b(u)∇u) in L2-norm are deduced for the semi-discrete and linearized fully-discrete systems (τ is the temporal partition parameter). What’s more, the new interpolated postprocessing operators are put forward and the corresponding global superconvergence results are obtained unconditionally, while previous literature always require certain time step conditions. Finally, some numerical results are provided to confirm our theoretical analysis, and show the efficiency of the method.