弱有限元方法在分数阶稳态方程上的应用  

Application of Weak Finite Element Method to Fractional Stationary Equation

作　　者：叶珊珊 张晓梅[2] 李伙友 YE Shanshan;ZHANG Xiaomei;LI Huoyou(Longyan University,Longyan,Fujian 364000,China)

机构地区：[1]龙岩学院数学与信息工程学院,福建龙岩364000 [2]龙岩学院,福建龙岩364000

出　　处：《龙岩学院学报》2022年第5期1-11,共11页Journal of Longyan University

摘　　要：首次提出弱有限元方法在分数阶稳态方程上的应用,在弱有限元空间中定义新的可以被分片多项式逼近的弱梯度算子和适合的范数,将基函数分成两部分:内部K、边界∂K,再加上稳定子s(v,w)来补偿单元边界的弱连续性,证明了解的存在唯一性。从误差估计的理论分析和数值实验结果两个角度说明了弱有限元方法在分数阶稳态方程上的可行性和诸多优点,比如弱有限元空间在满足稳定性和逼近要求的同时是容易构造的,即使在不连续元上数值计算也有很高的灵活性和有效性。This paper for the first time used the weak Galerkin finite element method in fractional stationary equations,which defined the norm and the weak gradient operator which can be approximate by piecewise polynomial.The basis function was divided into interior and boundary.The continuity was compensated by the stabilizer s(v,w)through a suitable boundary integral defined on the boundary of elements.Finally,the feasibility and many advantages of the weak finite element method in fractional stationary equations are illustrated from the theoretical analysis of error estimation and numerical experimental results,which demonstrate WG methods highly flexible and efficient in practical computation.

关 键 词：弱有限元方法 分数阶稳态方程 弱离散算子 弱有限元空间 多项式空间维度 

分 类 号：O242[理学—计算数学]