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Original Article

Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation

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Pages 1514-1531 | Received 18 Jan 2018, Accepted 17 Sep 2018, Published online: 02 Oct 2018
 

ABSTRACT

This paper concerns with the superconvergence analysis of a new mixed finite element method (MFEM) with element pair (Q11+Q01×Q10) for time-dependent nonlinear Schrödinger equation(NLSE). Based on the special characters of this element pair and the superclose estimate between the interpolation and projection operators in H1-norm together with a simple interpolation postprocessing approach, the superclose and global superconvergence results of the original and the flux variable are deduced for a linearized backward Euler fully-discrete scheme. Finally, some numerical results are provided to confirm the theoretical analysis.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant numbers 11671369; 11271340].

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