Conforming, nonconforming and DG methods for the stationary generalized Burgers- Huxley equation

TL;DR

This paper analyzes the stationary generalized Burgers-Huxley equation and introduces conforming, nonconforming, and DG finite element methods, providing theoretical analysis and computational validation of their effectiveness.

Contribution

It develops and compares three finite element methods for a nonlinear elliptic problem, including rigorous error estimates and solution analysis.

Findings

All three methods are effective for the problem.

Error estimates are rigorously derived for each scheme.

Computational results confirm the theoretical predictions.

Abstract

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.