Abstract In this paper, we present a continuous and discrete time weak Galerkin finite element method (WG-FEM) for solving two dimensional time fractional coupled Burgers' equations. The stability is proved for discrete time WG-FEM and the optimal order error in L 2 -norm is obtained based on fractional derivative definition, fractional integral definition and dual argument technique for continues and discrete time WG-FEM. The numerical example is to illustrate the theoretical analysis with polynomial mixture { P k ( K ) , P k − 1 ( ∂ K ) , [ P k − 1 ( K ) ] 2 } .

中文翻译：

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求解二维时间分形耦合汉堡方程的弱伽辽金有限元方法

摘要 在本文中，我们提出了一种用于求解二维时间分数耦合伯格斯方程的连续离散时间弱伽辽金有限元法（WG-FEM）。证明了离散时间WG-FEM的稳定性，并基于连续和离散时间WG-FEM的分数阶导数定义、分数积分定义和双参数技术得到了L 2 -范数的最优阶误差。数值例子是说明多项式混合{P k (K), P k − 1 (∂ K), [ P k − 1 ( K ) ] 2 }的理论分析。