Weak Galerkin finite element method for the nonlinear Schrodinger equation

	Weak Galerkin finite element method for the nonlinear Schrodinger equation
International Journal of Nonlinear Analysis and Applications
مقاله 198، دوره 13، شماره 2، مهر 2022، صفحه 2453-2468 اصل مقاله (721.85 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27518.3634
نویسندگان
Dalal Ismael Aziz؛ Ahmed J. Hussein^*
College of Education for Pure Sciences, University of Thi-Qar, Iraq
چکیده
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.
کلیدواژه‌ها
WGFEM؛ nonlinear Schrodinger equation؛ semi-discrete؛ Fully discrete (backward Euler scheme؛ Crank-Nicolson scheme)؛ error estimates
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