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首页> 外文期刊>International journal of computer mathematics >Superconvergence analysis of an H~1 -Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations
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Superconvergence analysis of an H~1 -Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations

机译：二维多维时间分数阶扩散方程H〜1 -Galerkin混合有限元方法的超收敛性分析

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摘要

In this paper, numerical approximation for two-dimensional (2D) multiterm time fractional diffusion equation is considered. By virtue of properties of bilinear element, Raviart-Thomas element and L1 approximation, an H-1-Galerkin mixed finite element fully discrete approximate scheme is established for 2D multi-term time fractional diffusion equation. And then, unconditionally stable of the approximate scheme is rigourously testified by dealing with fractional derivative skilfully. At the same time, superclose results for the original variable u in H-1-norm and the flux (q) over bar = del u in H(div, Omega)-norm are derived. Furthermore, the global superconvergence results for u in H-1-norm are deduced by the interpolation postprocessing operator. Finally, numerical results demonstrate that the approximate scheme provides a valid and efficient way for solving 2D multi-term time fractional diffusion equation.
机译：在本文中，考虑了二维（2D）多项式时间分数扩散方程的数值逼近。利用双线性元，Raviart-Thomas元和L1逼近的性质，建立了二维多项时间分数阶扩散方程的H-1-Galerkin混合有限元完全离散逼近方案。然后，巧妙地处理分数导数，严格证明了近似方案的无条件稳定。同时，推导了H-1-范数中原始变量u和H（div，Omega）范数中bar = del u上的通量（q）的超闭合结果。此外，通过插值后处理算子推导H-1-范数中u的全局超收敛结果。最后，数值结果表明，该近似方案为求解二维多项式时间分数阶扩散方程提供了有效而有效的方法。

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