Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations
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摘要: 研究了立方Schrödinger方程的二阶向后差分有限元方法(BDF2-FEM)的无条件最优误差估计.首先,将误差分为时间误差和空间误差两部分.通过引入时间离散方程,得到时间离散方程解的一致有界性,并给出时间误差估计.从而得到该方程在半隐格式下BDF2FEM无条件最优误差估计.最后,用数值算例验证了理论分析.
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关键词:
- 无条件收敛 /
- 向后Euler法 /
- Galerkin有限元方法 /
- Schrödinger方程
Abstract: The optimal error estimates of the semi-implicit BDF2-FEM were studied for cubic Schrödinger equations. First, an error estimate was divided into 2 parts: the temporal-discretization and the spatial-discretization. Through introduction of a temporal-discretization equation, the uniform boundedness of the solution and the temporal error estimate were obtained. The unconditionally optimal error estimates of the 2nd-order backward difference (BDF2-FEM) semi-implicit scheme for cubic Schrdinger equations were given. Finally, numerical examples verify the theoretical analysis. -
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