In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for its numerical approximation. The existence, uniqueness and regularity of weak solutions are discussed in detail using a Faedo-Galerkin approach and fixed-point theory, and a priori error estimates for all three types of numerical schemes are rigorously derived. A set of computational results are presented to show the efficacy of the proposed methods.

中文翻译：

---

平稳广义 Burgers-Huxley 方程的符合、不符合和 DG 方法

在这项工作中，我们解决了平稳广义 Burgers-Huxley 方程（具有异常对流的非线性椭圆问题）的分析，并提出了符合、非符合和不连续 Galerkin 有限元方法的数值近似。使用 Faedo-Galerkin 方法和不动点理论详细讨论了弱解的存在性、唯一性和规律性，并严格导出了所有三种数值方案的先验误差估计。提供了一组计算结果以显示所提出方法的有效性。