  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 is 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.
