Abstract
ABSTRACTIn this paper, we study a linearized Crank–Nicolson Galerkin finite element method for solving the nonlinear fractional Ginzburg–Landau equation. The boundedness, existence and uniqueness of the numerical solution are studied in details. Then we prove that the optimal error estimates hold unconditionally, in the sense that no restriction on the size of the time step in terms of the spatial mesh size needs to be assumed. Finally, numerical tests are investigated to support our theoretical analysis.
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