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Volume 6, Issue 2
Nonconforming Mixed Finite Element Method for the Stationary Conduction-Convection Problem

D. Shi & J. Ren

Int. J. Numer. Anal. Mod., 6 (2009), pp. 293-310.

Published online: 2009-06

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  • Abstract

In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature, respectively. The convergence analysis is presented and the optimal error estimates in a broken $H^1$-norm for the velocity, $L^2$-norm for the pressure and $H^1$-seminorm for the temperature are derived.

  • Keywords

Stationary conduction-convection problem, nonconforming mixed finite element, the optimal error estimates.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-293, author = {D. Shi and J. Ren}, title = {Nonconforming Mixed Finite Element Method for the Stationary Conduction-Convection Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {2}, pages = {293--310}, abstract = {

In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature, respectively. The convergence analysis is presented and the optimal error estimates in a broken $H^1$-norm for the velocity, $L^2$-norm for the pressure and $H^1$-seminorm for the temperature are derived.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/769.html} }
TY - JOUR T1 - Nonconforming Mixed Finite Element Method for the Stationary Conduction-Convection Problem AU - D. Shi & J. Ren JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 293 EP - 310 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/769.html KW - Stationary conduction-convection problem, nonconforming mixed finite element, the optimal error estimates. AB -

In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature, respectively. The convergence analysis is presented and the optimal error estimates in a broken $H^1$-norm for the velocity, $L^2$-norm for the pressure and $H^1$-seminorm for the temperature are derived.

D. Shi and J. Ren. (2009). Nonconforming Mixed Finite Element Method for the Stationary Conduction-Convection Problem. International Journal of Numerical Analysis and Modeling. 6 (2). 293-310. doi:
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