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Numerical Simulation of Two-Dimensional Pucci’s Equation with Dirichlet Boundary Conditions Using Nonvariational Finite Element Method

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Abstract

This paper provides numerical simulation of two-dimensional Pucci’s equation with Dirichlet boundary conditions. The Pucci’s operator is a prototype of a nonlinear operator in non-divergence form. Non-divergence form makes numerical solution challenging because standard tools like Pohozaev identity and global integration by parts are no longer applicable. Therefore, present study for the numerical solution relies on non-variational finite element method, which is independent of above said tools. After non-variational space discretization the resulting finite dimensional problem is solved by Newton iterative method.

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Acknowledgements

This research work is supported by financial grant No. 9/1032(0005)2K14-EMR-I sponsored by Council of Scientific and Industrial Research, New Delhi, Government of India.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, 211004, India

    Garima Mishra & Manoj Kumar

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  1. Garima Mishra
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  2. Manoj Kumar
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Correspondence to Manoj Kumar.

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Mishra, G., Kumar, M. Numerical Simulation of Two-Dimensional Pucci’s Equation with Dirichlet Boundary Conditions Using Nonvariational Finite Element Method. Differ Equ Dyn Syst 30, 353–362 (2022). https://doi.org/10.1007/s12591-018-0441-7

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  • DOI: https://doi.org/10.1007/s12591-018-0441-7

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