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Volume 27, Issue 4
Explicit Error Estimates for Mixed and Nonconforming Finite Elements

Shipeng Mao & Zhongci Shi

DOI: 10.4208/jcm.2009.27.4.011

J. Comp. Math., 27 (2009), pp. 425-440.

Published online: 2009-08

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  • Abstract

In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be extended to the nonconforming $P_1$ scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.

  • Keywords

Mixed finite element, Nonconforming finite element, Explicit error estimate, Maximal angle condition.

  • AMS Subject Headings

65N12, 65N15, 65N30, 65N50.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-425, author = {Mao , Shipeng and Shi , Zhongci}, title = {Explicit Error Estimates for Mixed and Nonconforming Finite Elements}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {4}, pages = {425--440}, abstract = {

In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be extended to the nonconforming $P_1$ scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.4.011}, url = {http://global-sci.org/intro/article_detail/jcm/8581.html} }
TY - JOUR T1 - Explicit Error Estimates for Mixed and Nonconforming Finite Elements AU - Mao , Shipeng AU - Shi , Zhongci JO - Journal of Computational Mathematics VL - 4 SP - 425 EP - 440 PY - 2009 DA - 2009/08 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.4.011 UR - https://global-sci.org/intro/article_detail/jcm/8581.html KW - Mixed finite element, Nonconforming finite element, Explicit error estimate, Maximal angle condition. AB -

In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be extended to the nonconforming $P_1$ scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.

Shipeng Mao & Zhongci Shi. (2019). Explicit Error Estimates for Mixed and Nonconforming Finite Elements. Journal of Computational Mathematics. 27 (4). 425-440. doi:10.4208/jcm.2009.27.4.011
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