In this article, we use the weak Galerkin (WG) finite element method to study a class of time fractional generalized Burgers' equation. The existence of numerical solutions and the stability of fully discrete scheme are proved. Meanwhile, by applying the energy method, an optimal order error estimate in discrete L² norm is established. Numerical experiments are presented to validate the theoretical analysis.

中文翻译：

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一类时间分数阶广义Burgers方程的弱Galerkin有限元方法

在本文中，我们使用弱Galerkin（WG）有限元方法来研究一类时间分数广义Burgers方程。证明了数值解的存在性和完全离散格式的稳定性。同时，通过应用能量方法，建立了离散L ²范数的最优阶误差估计。通过数值实验验证了理论分析的正确性。