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- Title
Unconditional superconvergent analysis of a new mixed finite element method for Ginzburg–Landau equation.
- Authors
Shi, Dongyang; Liu, Qian
- Abstract
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 (Q11/Q01 × Q10). 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(h2 + τ) for u in H1‐norm and p = ∇u in L2‐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.
- Subjects
FINITE element method; LANDAU theory; DISCRETE systems; SUPERCONVERGENT methods; SAMPLING errors
- Publication
Numerical Methods for Partial Differential Equations, 2019, Vol 35, Issue 1, p422
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22307