In this paper, the numerical approximation of the generalized Burgers'-Huxley equation (GBHE) with weakly singular kernels using non-conforming methods will be presented. Specifically, we discuss two new formulations. The first formulation is based on the non-conforming finite element method (NCFEM). The other formulation is based on discontinuous Galerkin finite element methods (DGFEM). The wellposedness results for both formulations are proved. Then, a priori error estimates for both the semi-discrete and fully-discrete schemes are derived. Specific numerical examples, including some applications for the GBHE with weakly singular model, are discussed to validate the theoretical results.

翻译：本文研究采用非协调方法数值逼近具有弱奇异核的广义Burgers-Huxley方程（GBHE）。具体而言，我们讨论两种新格式。第一种格式基于非协调有限元方法（NCFEM），另一种格式基于间断Galerkin有限元方法（DGFEM）。证明了两种格式的适定性结果，并推导了半离散和全离散格式的先验误差估计。通过具体的数值算例（包括弱奇异GBHE模型的部分应用）验证理论结果。