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 () 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 -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.

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