Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation

ABSTRACT

This paper concerns with the superconvergence analysis of a new mixed finite element method (MFEM) with element pair ($Q_{11}+Q_{01}\times Q_{10}$) 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 $H^1$-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.

KEYWORDS:

• Nonlinear Schrödinger equation
• new mixed FEM
• special characters
• superclose property
• superconvergence results

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N30
• 65N12
• 35K61

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].