Premium
Unconditional superconvergent analysis of a new mixed finite element method for Ginzburg–Landau equation
Author(s) -
Shi Dongyang,
Liu Qian
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22307
Subject(s) - superconvergence , mathematics , bilinear interpolation , finite element method , norm (philosophy) , mixed finite element method , subdivision , mathematical analysis , statistics , physics , law , history , archaeology , political science , thermodynamics
In this article, unconditional superconvergent analysis of a linearized fully discrete mixed finite element method is presented for a class of Ginzburg–Landau equation based on the bilinear element and zero‐order Nédélec's element pair ( Q 11 / Q 01 × Q 10 ). First, a time‐discrete system is introduced to split the error into temporal error and spatial error, and the corresponding error estimates are deduced rigorously. Second, the unconditional superclose and optimal estimate of order O ( h 2 + τ ) for u in H 1 ‐norm and p = ∇ u in L 2 ‐norm are derived respectively without the restrictions on the ratio between h and τ , where h is the subdivision parameter and τ , the time step. Third, the global superconvergent results are obtained by interpolated postprocessing technique. Finally, some numerical results are carried out to confirm the theoretical analysis.