A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation

Xiaohui Hu; Pengzhan Huang; Xinlong Feng

Applications of Mathematics (2016)

  • Volume: 61, Issue: 1, page 27-45
  • ISSN: 0862-7940

Abstract

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In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the P 0 2 - P 1 pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.

How to cite

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Hu, Xiaohui, Huang, Pengzhan, and Feng, Xinlong. "A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation." Applications of Mathematics 61.1 (2016): 27-45. <http://eudml.org/doc/276246>.

@article{Hu2016,
abstract = {In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the $P_0^2-P_1$ pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.},
author = {Hu, Xiaohui, Huang, Pengzhan, Feng, Xinlong},
journal = {Applications of Mathematics},
keywords = {Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition; Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition},
language = {eng},
number = {1},
pages = {27-45},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation},
url = {http://eudml.org/doc/276246},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Hu, Xiaohui
AU - Huang, Pengzhan
AU - Feng, Xinlong
TI - A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 27
EP - 45
AB - In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the $P_0^2-P_1$ pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.
LA - eng
KW - Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition; Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition
UR - http://eudml.org/doc/276246
ER -

References

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