Finite element approximation for the delayed generalized Burgers-Huxley equation with weakly singular kernel: Part II Non-Conforming and DG approximation
Numerical Analysis
2023-11-02 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2310.07788,
title = {Finite element approximation for the delayed generalized Burgers-Huxley equation with weakly singular kernel: Part II Non-Conforming and DG approximation},
author = {Sumit Mahajan and Arbaz Khan},
journal= {arXiv preprint arXiv:2310.07788},
year = {2023}
}