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Weighted extended B-spline finite element analysis of a coupled system of general elliptic equations

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Abstract

In this study we establish the existence and uniqueness of the solution of a coupled system of general elliptic equations with anisotropic diffusion, non-uniform advection and variably influencing reaction terms on Lipschitz continuous domain \({\varOmega }\subset {\mathbb {R}}^m \) (\(\hbox {m}\ge 1\)) with a Dirichlet boundary. Later we consider the finite element (FE) approximation of the coupled equations in a meshless framework based on weighted extended B-Spine functions. The a priori error estimates corresponding to the finite element analysis are derived to establish the convergence of the corresponding finite element scheme and the numerical methodology has been tested on a example.

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Acknowledgements

The authors would like to express their gratitude to Dr.Klaus Hoellig and Joerg Hoerner for helping us in modifying the Matlab code. The Ph.D. Fellowship of NBHM-DAE is gratefully acknowledged by the first author.

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Authors and Affiliations

  1. Faculty Building, Indian Institute of Technology Kanpur, Kanpur, 208016, Uttar Pradesh, India

    Ayan Chakraborty & B. V. Rathish Kumar

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  1. Ayan Chakraborty
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  2. B. V. Rathish Kumar
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Correspondence to B. V. Rathish Kumar.

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Chakraborty, A., Kumar, B.V.R. Weighted extended B-spline finite element analysis of a coupled system of general elliptic equations. Int J Adv Eng Sci Appl Math 10, 34–40 (2018). https://doi.org/10.1007/s12572-018-0205-1

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  • DOI: https://doi.org/10.1007/s12572-018-0205-1

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