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

作者：Shi Dongyang^*; Yan Fengna; Wang Junjun

来源：Applied Mathematics and Computation, 2016, 274: 182-194.

DOI：10.1016/j.amc.2015.09.004

• Nonlinear Sobolev equation
• Mixed finite element method
• Semi-discrete and fully-discrete schemes
• tau-independent superclose and superconvergence results

In this paper, a new mixed finite element scheme is proposed for the nonlinear Sobolev equation by employing the finite element pair Q(11)/Q(01) x Q(10). Based on the combination of interpolation and projection skill as well as the mean-value technique, the tau-independent superclose results of the original variable u in H-1-norm and the variable View the (q) over right arrow = -(a(u)del u(t)+b(u)del u) in L-2-norm are deduced for the semi-discrete and linearized fully-discrete systems (? is the temporal partition parameter). Whats 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.

• 出版日期2016-2-1
• 单位郑州大学