修正RLW方程的一种混合有限元方法的数值分析与模拟
The Numerical Analysis and Simulation Based on A Mixed Finite Element Method for the MRLW Equation
摘要: 本文针对修正的RLW方程提出并讨论了一种二阶向后差分的混合有限元方法。在空间方向上使用混合Galerkin有限元方法来近似，在时间上采用向后差q = ux分二阶离散格式来近似。并且得到了方程的未知解u在L2模和H1模下的最优误差估计以及在L2模下的最优误差估计。为了对数值理论进行有效性验证，我们通过一些数值算例给出一些数值模拟结果。
Abstract: A second-order backward-difference mixed finite element (MFE) method for modified regularized long wave (MRLW) equation is proposed and discussed in this paper. The spatial direction is approximated by the mixed Galerkin method using mixed linear space finite elements, and the time direction is considered by backward difference scheme with second-order convergence rate. The optimal error estimates for u in L2 and H1-norms and its flux q = ux and in L2-norm are derived. Some numerical results are given to test our theoretical analysis and illustrate the efficiency of the studied method.
文章引用：樊恩宇. 修正RLW方程的一种混合有限元方法的数值分析与模拟[J]. 应用数学进展, 2019, 8(12): 2096-2107. https://doi.org/10.12677/AAM.2019.812240

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