Error Estimates in the Maximum Norm for the Solution of Poisson’s Equation Approximated by the Five-Point Laplacian Using the Discrete Maximum Principle

Authors

  • Ganesh Bahadur Basnet Department of Mathematics, Tribhuvan University, Tri-Chandra Multiple Campus, Kathmandu, Nepa
  • Madhav Prasad Poudel School of Engineering, Pokhara University, Pokhara, Nepal
  • Resham Prasad Paudel Department of Mathematics, Tribhuvan University, Tri-Chandra Multiple Campus, Kathmandu, Nepal

DOI:

https://doi.org/10.3126/jnms.v6i2.63020

Keywords:

Maximum principle, Poisson’s equation, Laplacian, Maximum norm, Error estimates

Abstract

In this paper, we study error estimates in the maximum norm in the context of solving Poisson’s equation numerically when approximated the Five-Point Laplacian method using the discrete maximum principle. The primary objective is to assess the accuracy of this numerical approach in solving Poisson’s equation and to provide insights into the behavior of error estimates. We focus on the estimates of maximum norm of the discrete functions defined on a grid in a unit square as well as in a square of side s, and estimate errors measured in the maximum norm.

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Published

2024-02-26

How to Cite

Basnet, G. B., Poudel, M. P., & Paudel, R. P. (2024). Error Estimates in the Maximum Norm for the Solution of Poisson’s Equation Approximated by the Five-Point Laplacian Using the Discrete Maximum Principle. Journal of Nepal Mathematical Society, 6(2), 28–37. https://doi.org/10.3126/jnms.v6i2.63020

Issue

Vol. 6 No. 2 (2024)

Section

Articles

License

© Nepal Mathematical Society