【摘要】 主要讨论二维多项时间分数阶扩散方程的H¹-Galerkin混合元方法.空间上借助不完全双二次元和一阶BDFM元，时间方向上利用修正的L1格式，建立了该方程的全离散逼近格式.首先证明了该格式的稳定性.然后借助单元性质和已有的高精度结果，得到了原始变量在H¹模意义下和中间变量在H（div,Ω）模意义下具有O(h³+τ^2-α_s)的超逼近结果，这里h为空间步长，τ为时间步长，α_s为分数阶微分算子的最高阶数.更多还原

【Abstract】 The H1-Galerkin mixed finite element method is applied to two-dimensional multiterm time fractional diffusion equation.By use of a modified L1 scheme in time direction and incomplete biquadratic element and one order BDFM element in space direction, the according fully-discrete scheme is constructed.Firstly, the stability is proved.And then applying the element properties and the existing high accuracy results, the superclose results of order O(h³+τ^2-α_s)for the primitive variable in H¹-norm and the intermediate variable in H（div,Ω）-norm are deduced.更多还原