Finite Element Approximation for the Delayed Generalized Burgers–Huxley Equation with Weakly Singular Kernel: Part II Nonconforming and DG Approximation

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page A2972-A2998, October 2024.
Abstract. In this paper, the numerical approximation of the generalized Burgers–Huxley equation (GBHE) with weakly singular kernels using nonconforming methods will be presented. Specifically, we discuss two new formulations. The first formulation is based on the nonconforming finite element method. The other formulation is based on discontinuous Galerkin finite element methods. The wellposedness results for both formulations are proved. Then, a priori error estimates for both the semidiscrete and fully discrete schemes are derived. Specific numerical examples, including some applications for the GBHE with a weakly singular model, are discussed to validate the theoretical results.