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

Authors

  • 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.

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Published

2023-01-30

How to Cite

Poonepalle, A., Shi, B., Kang, E. ., Chin, J. ., Singh, M. ., Gupta, P. ., … 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