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

2021/01/12 by Arbaz Khan, Khan, Arbaz, Manil T. Mohan +3 · 1 citation
Engineering · Mathematics · #35J66 #65J15 #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2101.04665

openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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