多项时间混合分数阶扩散波动方程的类Wilson非协调元超收敛分析  

Superconvergence Analysis of Quasi-Wilson Nonconforming Finite Element for Multi-Term Time Fractional Mixed Diffusion Wave Equation

作　　者：樊明智[1] 赵艳敏 王芬玲[1] 史艳华[1] 范慧君 FAN Ming-zhi;ZHAO Yan-min;WANG Fen-ling;SHI Yan-hua;FAN Hui-jun(School of Science,Xuchang University,Xuchang 461000,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]许昌学院数理学院,河南许昌461000 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《数学的实践与认识》2024年第10期130-143,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11971416);河南省高等学校重点科研项目(22A110022)。

摘　　要：基于时间方向采用混合有限差分近似和空间方向选取类Wilson非协调有限元逼近,对带时-空耦合导数的多项时间混合分数阶扩散波动方程建立了全离散高效数值格式.首先,证明了全离散格式的解在能量模意义下的无条件稳定性.然后,利用该元的相容误差估计在L^(2)模意义下可以达到二阶精度和该元协调部分的高精度结果,并借助于双线性插值算子代替传统有限元分析中不可缺少的Ritz投影及插值后处理技术,导出了全离散格式下的超逼近性和超收敛结果.最后,运用数值实验模拟分析,验证了理论分析的正确性.Based on the mixed finite difference approximation in time and the quasi-wilson nonconforming finite element approximation in space,a efficient fully discrete numerical scheme is established for the multi-term time fractional mixed diffusion wave equation with time-space coupling derivatives.Firstly,the unconditional stability of the solution of the fully discrete scheme in the energy norm sense is proved.Then,the consistent error estimate that can reach second-order accuracy under L^(2)-norm and the high-accuracy result of the conforming finite element part be used.By means of bilinear interpolation operator instead of the indispensable Ritz projection in the traditional finite element analysis and interpolation post-processing techniques,the superclose and superconvergence results in the fully discrete scheme are derived.Finally,numerical experiments are used to verify the correctness of the theoretical analysis.

关 键 词：多项时间混合分数阶扩散波动方程 类Wilson非协调有限元 全离散格式 无条件稳定 超逼近和超收敛 

分 类 号：O241.82[理学—计算数学]