The Mixed Finite Element Method Based on the Crank-Nicolson Scheme for Darcy Flows in Porous Media

  • Akshaya Poonepalle Lambert High School
  • Brent Shi Atlanta International School
  • Elly Kang Marist School
  • Joseph Chin North Gwinnett High School
  • Mannan Singh Lambert High School
  • Prakhar Gupta South Forsyth High School
  • Riya Malhotra South Forsyth High School
  • Sanjana Kadiyala Milton High school
  • Sirihansika Thadiparthi South Forsyth High School
  • Thinh Kieu University of North Georgia
  • Yeeun Kim Gwinnett School of Mathematics, Science, and Technology
DOI: https://doi.org/10.46787/pump.v6i0.3331
Keywords: mixed finite element method; Crank--Nicolson scheme; error estimates; optimal order

Abstract

This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the Darcy flows. Optimal order error estimates in two different norms are established for the lowest order. Numerical experiments confirm the theoretical analysis regarding convergence rates.

Published
2023-01-30
How to Cite
Poonepalle, A., Shi, B., Kang, E., Chin, J., Singh, M., Gupta, P., Malhotra, R., Kadiyala, S., Thadiparthi, S., Kieu, T., & Kim, Y. (2023). The Mixed Finite Element Method Based on the Crank-Nicolson Scheme for Darcy Flows in Porous Media. The PUMP Journal of Undergraduate Research, 6, 40-58. https://doi.org/10.46787/pump.v6i0.3331
Issue
Vol. 6 (2023): PUMP Journal of Undergraduate Research
Section
Articles

Copyright (c) 2023 Akshaya Poonepalle, Brent Shi, Elly Kang, Joseph Chin, Mannan Singh, Prakhar Gupta, Riya Malhotra, Sanjana Kadiyala, Sirihansika Thadiparthi, Thinh Kieu, Yeeun Kim

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.