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Volume 33, Issue 3
A Canonical Construction of $H^m$-Nonconforming Triangular Finite Elements

Jun Hu & Shangyou Zhang

Ann. Appl. Math., 33 (2017), pp. 266-288.

Published online: 2022-06

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  • Abstract

We design a family of 2D $H^m$-nonconforming finite elements using the full $P_{2m−3}$ degree polynomial space, for solving $2m$th elliptic partial differential equations. The consistent error is estimated and the optimal order of convergence is proved. Numerical tests on the new elements for solving tri-harmonic, 4-harmonic, 5-harmonic and 6-harmonic equations are presented, to verify the theory.

  • Keywords

nonconforming finite element, minimum element, high order partial differential equation.

  • AMS Subject Headings

65N30, 73C02

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-33-266, author = {Hu , Jun and Zhang , Shangyou}, title = {A Canonical Construction of $H^m$-Nonconforming Triangular Finite Elements}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {33}, number = {3}, pages = {266--288}, abstract = {

We design a family of 2D $H^m$-nonconforming finite elements using the full $P_{2m−3}$ degree polynomial space, for solving $2m$th elliptic partial differential equations. The consistent error is estimated and the optimal order of convergence is proved. Numerical tests on the new elements for solving tri-harmonic, 4-harmonic, 5-harmonic and 6-harmonic equations are presented, to verify the theory.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20610.html} }
TY - JOUR T1 - A Canonical Construction of $H^m$-Nonconforming Triangular Finite Elements AU - Hu , Jun AU - Zhang , Shangyou JO - Annals of Applied Mathematics VL - 3 SP - 266 EP - 288 PY - 2022 DA - 2022/06 SN - 33 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20610.html KW - nonconforming finite element, minimum element, high order partial differential equation. AB -

We design a family of 2D $H^m$-nonconforming finite elements using the full $P_{2m−3}$ degree polynomial space, for solving $2m$th elliptic partial differential equations. The consistent error is estimated and the optimal order of convergence is proved. Numerical tests on the new elements for solving tri-harmonic, 4-harmonic, 5-harmonic and 6-harmonic equations are presented, to verify the theory.

Jun Hu & Shangyou Zhang. (2022). A Canonical Construction of $H^m$-Nonconforming Triangular Finite Elements. Annals of Applied Mathematics. 33 (3). 266-288. doi:
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