scholarly journals A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations

2019 ◽  
Vol 88 (320) ◽  
pp. 2793-2825
Author(s):  
Raphael Kruse ◽  
Yue Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Fully Discrete ◽  
Element Method

Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation

2017 ◽  
Vol 10 (3) ◽  
pp. 671-688 ◽  
Author(s):  
Jianyun Wang ◽  
Yunqing Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Fully Discrete ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Element Method

AbstractThis paper is concerned with numerical method for a two-dimensional time-dependent cubic nonlinear Schrödinger equation. The approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time, respectively. We prove optimalL2error estimates for two fully discrete schemes by using elliptic projection operator. Finally, a numerical example is provided to verify our theoretical results.

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