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Conforming, Nonconforming and DG Methods for the Stationary Generalized Burgers-Huxley Equation

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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 are 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.

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Acknowledgements

AK has been supported by the Sponsored Research & Industrial Consultancy (SRIC), Indian Institute of Technology Roorkee, India through the faculty initiation grant MTD/FIG/100878; MTM has been supported by the Department of Science and Technology (DST), India through the Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award IFA17-MA110; and RRB has been supported by the Monash Mathematics Research Fund S05802-3951284, by the HPC-Europa3 Transnational Access programme through grant HPC175QA9K, and by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers “Digital biodesign and personalised healthcare” No. 075-15-2020-926.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee (IITR), Roorkee, 247667, India

    Arbaz Khan & Manil T. Mohan

  2. School of Mathematics, Monash University, 9 Rainforest Walk, Melbourne, VIC, 3800, Australia

    Ricardo Ruiz-Baier

  3. Institute of Computer Science and Mathematical Modelling, Sechenov University, Moscow, Russian Federation

    Ricardo Ruiz-Baier

  4. Universidad Adventista de Chile, Casilla 7-D, Chillán, Chile

    Ricardo Ruiz-Baier

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  1. Arbaz Khan
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Correspondence to Arbaz Khan.

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Khan, A., Mohan, M.T. & Ruiz-Baier, R. Conforming, Nonconforming and DG Methods for the Stationary Generalized Burgers-Huxley Equation. J Sci Comput 88, 52 (2021). https://doi.org/10.1007/s10915-021-01563-3

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