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Non Uniform Weighted Extended B-Spline Finite Element Analysis of Non Linear Elliptic Partial Differential Equations

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Abstract

We propose a non uniform web spline based finite element analysis for elliptic partial differential equation with the gradient type nonlinearity in their principal coefficients like p-laplacian equation and Quasi-Newtonian fluid flow equations. We discuss the well-posednes of the problems and also derive the apriori error estimates for the proposed finite element analysis and obtain convergence rate of \(\mathcal {O}(h^{\alpha })\) for \(\alpha > 0\).

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Acknowledgements

The authors are grateful to the reviewers for their careful reading and intuitive implications.

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Authors and Affiliations

  1. IIT Kanpur, Kanpur, India

    Ayan Chakraborty

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

    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. Non Uniform Weighted Extended B-Spline Finite Element Analysis of Non Linear Elliptic Partial Differential Equations. Differ Equ Dyn Syst 30, 485–497 (2022). https://doi.org/10.1007/s12591-020-00557-1

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