CONSERVATIVE CONFORMING AND NONCONFORMING VEMS FOR FOURTH ORDER NONLINEAR SCHRODINGER EQUATIONS WITH TRAPPED TERM  

作　　者：Meng Li Jikun Zhao Zhongchi Wang Shaochun Chen 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China [2]School of Computer Science and Engineering,Beihang university,Beijing 100083,China

出　　处：《Journal of Computational Mathematics》2024年第2期454-499,共46页计算数学（英文）

基　　金：supported by the NSF of China(Grant Nos.11801527,11701522,11771163,11671160,1191101330);by the China Postdoctoral Science Foundation(Grant No.2018M632791);by the Key Scientific Research Projects of Higher Eduction of Henan(Grant No.19A110034).

摘　　要：This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger 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.

关 键 词：H^(2)conforming virtual element C^(0)nonconforming virtual element Morleytype nonconforming virtual element Nonlinear Schrodinger equation Conservation Convergence 

分 类 号：O17[理学—数学]