带变系数时间分数阶扩散方程一个新的非协调高阶逼近格式高精度分析新模式  

A New Pattern of High Accuracy Analysis of Nonconforming High Order Approximation Scheme for the Time Fractional Diffusion Equations with Variable Coefficients

作　　者：王芬玲[1] 赵艳敏 史艳华[1] 魏亚冰 WANG Fenling;ZHAO Yanmin;SHI Yanhua;WEI Yabing(School of Science,Xuchang University,Xuchang 461000,China;School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]许昌学院数理学院,河南许昌461000 [2]江苏大学数学科学学院,江苏镇江212013

出　　处：《应用数学》2024年第4期1163-1172,共10页Mathematica Applicata

基　　金：国家自然科学基金(11971416);河南省高校科技创新团队支持计划项目(23IRTSTHN018)。

摘　　要：基于时间高阶L2-1_(σ)格式和空间EQ_(1)^(rot)非协调有限元方法,对带有变系数的一类时间分数阶扩散方程进行了高效数值分析.首先,证明全离散逼近格式的解在能量模意义下的无条件稳定性.然后,利用该元的特殊性质,并将插值算子和投影算子相结合,导出了采用传统估计无法导出的超逼近结果.此外,利用插值后处理技术,呈现了整体超收敛估计.最后,借助数值实验,验证了理论分析的正确性.Based on the high order L2-1_(σ)scheme in time and the non-conforming EQ_(1)^(rot) finite element method in space,a class of time-fractional diffusion equations with variable coefficients is numerically analyzed efficiently.Firstly,the unconditional stability of the solutions of the fully discrete approximation scheme is proved in the sense of energy norm.Then,by using the special property of this element and combining the interpolation operator and the projection operator,we derive the superclose result which cannot be derived by traditional estimation.In addition,the global superconvergence estimate is presented using interpolation postprocessing technique.Finally,the correctness of the theoretical analysis is verified through numerical experiments.

关 键 词：EQ_(1)^(rot)非协调元 全离散格式 无条件稳定 超逼近和超收敛 

分 类 号：O242.21[理学—计算数学]