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- W4322102571 abstract "In this paper, we study, analyze and numerically validate a conservative relaxation-type linear finite element method (FEM) for the nonlinear Schrödinger equation. The method avoids solving the complex nonlinear system and preserves the discrete mass and energy. A key to our analysis is that the errors are split into the temporal error and the spatial error by introducing the corresponding time-discrete system. Therefore, we derive the optimal L2 and semi-H1 error estimates without any coupling condition between time step τ and space size h. Some numerical experiments not only demonstrate the method’s optimal convergence rates but also confirm the conservation laws during long time simulations." @default.
- W4322102571 created "2023-02-26" @default.
- W4322102571 creator A5020948241 @default.
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- W4322102571 date "2023-08-01" @default.
- W4322102571 modified "2023-09-27" @default.
- W4322102571 title "Optimal a priori error estimate of relaxation-type linear finite element method for nonlinear Schrödinger equation" @default.
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- W4322102571 doi "https://doi.org/10.1016/j.cam.2023.115147" @default.
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