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Volume 27, Issue 6
A Posteriori Error Estimates of a Non-Conforming Finite Element Method for Problems with Artificial Boundary Conditions

Xianmin Xu & Zhiping Li

DOI: 10.4208/jcm.2009.09-m2608

J. Comp. Math., 27 (2009), pp. 677-696.

Published online: 2018-09

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  • Abstract

An a posteriori error estimator is obtained for a nonconforming finite element approximation of a linear elliptic problem, which is derived from a corresponding unbounded domain problem by applying a nonlocal approximate artificial boundary condition. Our method can be easily extended to obtain a class of a posteriori error estimators for various conforming and nonconforming finite element approximations of problems with different artificial boundary conditions. The reliability and efficiency of our a posteriori error estimator are rigorously proved and are verified by numerical examples.

  • Keywords

a posteriori estimate, nonconforming finite element method, artificial boundary conditions.

  • AMS Subject Headings

65N15, 65N30, 65N38.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-27-677, author = {Xianmin Xu and Zhiping Li}, title = {A Posteriori Error Estimates of a Non-Conforming Finite Element Method for Problems with Artificial Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {27}, number = {6}, pages = {677--696}, abstract = {

An a posteriori error estimator is obtained for a nonconforming finite element approximation of a linear elliptic problem, which is derived from a corresponding unbounded domain problem by applying a nonlocal approximate artificial boundary condition. Our method can be easily extended to obtain a class of a posteriori error estimators for various conforming and nonconforming finite element approximations of problems with different artificial boundary conditions. The reliability and efficiency of our a posteriori error estimator are rigorously proved and are verified by numerical examples.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2608}, url = {http://global-sci.org/intro/article_detail/jcm/12711.html} }
TY - JOUR T1 - A Posteriori Error Estimates of a Non-Conforming Finite Element Method for Problems with Artificial Boundary Conditions AU - Xianmin Xu & Zhiping Li JO - Journal of Computational Mathematics VL - 6 SP - 677 EP - 696 PY - 2018 DA - 2018/09 SN - 27 DO - http://doi.org/10.4208/jcm.2009.09-m2608 UR - https://global-sci.org/intro/article_detail/jcm/12711.html KW - a posteriori estimate, nonconforming finite element method, artificial boundary conditions. AB -

An a posteriori error estimator is obtained for a nonconforming finite element approximation of a linear elliptic problem, which is derived from a corresponding unbounded domain problem by applying a nonlocal approximate artificial boundary condition. Our method can be easily extended to obtain a class of a posteriori error estimators for various conforming and nonconforming finite element approximations of problems with different artificial boundary conditions. The reliability and efficiency of our a posteriori error estimator are rigorously proved and are verified by numerical examples.

Xianmin Xu and Zhiping Li. (2018). A Posteriori Error Estimates of a Non-Conforming Finite Element Method for Problems with Artificial Boundary Conditions. Journal of Computational Mathematics. 27 (6). 677-696. doi:10.4208/jcm.2009.09-m2608
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