Volume 18, Issue 3
The L2-Norm Error Estimate of Nonconforming Finite Element Method for the 2nd Order Elliptic Problem with the Lowest Regularity

J. Comp. Math., 18 (2000), pp. 277-282.

Published online: 2000-06

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• Abstract

The abstract $L^2$-norm error estimate of nonconforming finite element method is established. The uniformly $L^2$-norm error estimate is obtained for the nonconforming finite element method for the second order elliptic problem with the lowest regularity, i.e., in the case that the solution $u∈H^1(Ω)$ only. It is also shown that the $L^2$-norm error bound we obtained is one order higher than the energe-norm error bound.

• Keywords

$L^2$-norm error estimate, nonconforming f.e.m., lowest regularity.

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@Article{JCM-18-277, author = {Wang , Lie-Heng}, title = {The L2-Norm Error Estimate of Nonconforming Finite Element Method for the 2nd Order Elliptic Problem with the Lowest Regularity}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {3}, pages = {277--282}, abstract = {

The abstract $L^2$-norm error estimate of nonconforming finite element method is established. The uniformly $L^2$-norm error estimate is obtained for the nonconforming finite element method for the second order elliptic problem with the lowest regularity, i.e., in the case that the solution $u∈H^1(Ω)$ only. It is also shown that the $L^2$-norm error bound we obtained is one order higher than the energe-norm error bound.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9041.html} }
TY - JOUR T1 - The L2-Norm Error Estimate of Nonconforming Finite Element Method for the 2nd Order Elliptic Problem with the Lowest Regularity AU - Wang , Lie-Heng JO - Journal of Computational Mathematics VL - 3 SP - 277 EP - 282 PY - 2000 DA - 2000/06 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9041.html KW - $L^2$-norm error estimate, nonconforming f.e.m., lowest regularity. AB -

The abstract $L^2$-norm error estimate of nonconforming finite element method is established. The uniformly $L^2$-norm error estimate is obtained for the nonconforming finite element method for the second order elliptic problem with the lowest regularity, i.e., in the case that the solution $u∈H^1(Ω)$ only. It is also shown that the $L^2$-norm error bound we obtained is one order higher than the energe-norm error bound.

Lie-Heng Wang. (1970). The L2-Norm Error Estimate of Nonconforming Finite Element Method for the 2nd Order Elliptic Problem with the Lowest Regularity. Journal of Computational Mathematics. 18 (3). 277-282. doi:
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