正则长波Burgers方程的混合有限体积元方法
Mixed Finite Volume Element Method for Regularized Long Wave Burgers Equation
摘要: 本文研究了正则长波Burgers方程的混合有限体积元方法。引入迁移算子把试探函数空间映射为检验函数空间，构造了半离散和线性向后Euler全离散混合有限体积元格式，证明了两种离散格式解的存在唯一性，并得到了最优阶误差估计。最后，给出数值算例来验证理论分析结果和数值格式的有效性。
Abstract: The mixed finite volume element method for the regularized long wave Burgers equation is de-veloped and studied. By introducing a transfer operator which maps the trial function space into the test function space, the semi-discrete and linear backward Euler fully discrete mixed finite volume element schemes are constructed. Stability analysis for semi-discrete scheme is given, the existence and uniqueness of the solutions are proved, and optimal error estimates for these schemes are obtained. Finally, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed schemes.
文章引用：白雪, 李宏, 方志朝. 正则长波Burgers方程的混合有限体积元方法[J]. 应用数学进展, 2018, 7(3): 257-268. https://doi.org/10.12677/AAM.2018.73032

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