(untitled) (Journal of Computational Mathematics, 2024)
This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrödinger equations with trapped term. We mainly consider three types of virtual elements, including H^2 conforming virtual element, C^0 nonconforming virtual element and Morley-type nonconforming virtual element. The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time. We prove the mass and energy conservation, the boundedness and the unique solvability of the fully discrete schemes. After introducing a new type of the Ritz projection, the optimal and unconditional error estimates for the fully discrete schemes are presented and proved. Finally, two numerical examples are investigated to confirm our theoretical analysis.