CONVERGENCE ANALYSIS OF NONCONFORMING QUADRILATERAL FINITE ELEMENT METHODS FOR NONLINEAR COUPLED SCHRODINGER-HELMHOLTZ EQUATIONS  

作　　者：Dongyang Shi Houchao Zhang 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China

出　　处：《Journal of Computational Mathematics》2024年第4期979-998,共20页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12071443);by the Key Scientific Research Projects of Henan Colleges and Universities(Grant No.20B110013).

摘　　要：The focus of this paper is on two novel linearized Crank-Nicolson schemes with nonconforming quadrilateral finite element methods(FEMs)for the nonlinear coupled Schrodinger-Helmholtz equations.Optimal L^(2) and H^(1) estimates of orders O(h^(2)+τ^(2))and O(h^(2)+τ^(2))are derived respectively without any grid-ratio condition through the following two keys.One is that a time-discrete system is introduced to split the error into the temporal error and the spatial error,which leads to optimal temporal error estimates of order O(τ^(2))in L^(2) and the broken H^(1)-norms,as well as the uniform boundness of numerical solutions in L^(∞) norm.The other is that a novel projection is utilized,which can iron out the difficulty of the existence of the consistency errors.This leads to derive optimal spatial error estimates of orders O(h^(2))in L^(2)-norm and O(h)in the broken H^(1)-norm under the H^(2) regularity of the solutions for the time-discrete system.At last,two numerical examples are provided to confirm the theoretical analysis.Here,h is the subdivision parameter,and τ is the time step.

关 键 词：Schrodinger-Helmholtz equations Nonconforming FEMs Linearized Crank-Nicolson scheme Optimal error estimates 

分 类 号：O17[理学—数学]