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Volume 30, Issue 4
Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods

Carsten Carstensen, Joscha Gedicke & Donsub Rim

DOI: 10.4208/jcm.1108-m3677

J. Comp. Math., 30 (2012), pp. 337-353.

Published online: 2012-08

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  • Abstract

The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and Raviart-Thomas mixed finite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.

  • Keywords

Error estimates, Conforming, Nonconforming, Mixed, Finite element method.

  • AMS Subject Headings

65N15, 65N12, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-337, author = {Carsten Carstensen, Joscha Gedicke and Donsub Rim}, title = {Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {4}, pages = {337--353}, abstract = {

The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and Raviart-Thomas mixed finite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1108-m3677}, url = {http://global-sci.org/intro/article_detail/jcm/8435.html} }
TY - JOUR T1 - Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods AU - Carsten Carstensen, Joscha Gedicke & Donsub Rim JO - Journal of Computational Mathematics VL - 4 SP - 337 EP - 353 PY - 2012 DA - 2012/08 SN - 30 DO - http://doi.org/10.4208/jcm.1108-m3677 UR - https://global-sci.org/intro/article_detail/jcm/8435.html KW - Error estimates, Conforming, Nonconforming, Mixed, Finite element method. AB -

The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and Raviart-Thomas mixed finite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.

Carsten Carstensen, Joscha Gedicke and Donsub Rim. (2012). Explicit Error Estimates for Courant, Crouzeix-Raviart and Raviart-Thomas Finite Element Methods. Journal of Computational Mathematics. 30 (4). 337-353. doi:10.4208/jcm.1108-m3677
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