International Journal of Nonlinear Analysis and Applications

Weak Galerkin finite element method for the nonlinear Schrodinger equation

Document Type : Research Paper

Authors

College of Education for Pure Sciences, University of Thi-Qar, Iraq

Abstract

The numerical technique for a two-dimensional time-dependent nonlinear Schrodinger equation is the subject of this work. The approximations are produced using the weak Galerkin finite element technique with semi-discrete and fully discrete finite element methods, respectively, using the backward Euler method and the crank-Nicolson method in time. Using the elliptic projection operator, we provide optimum $L^{2}$ error estimates for semi and fully discrete weak Galerkin finite elements. Finally, we present numerical examples provided to verify our theoretical results.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 2453-2468
  • Receive Date: 03 January 2022
  • Revise Date: 19 February 2022
  • Accept Date: 12 March 2022