Volume 8, Issue 3
A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations

Sufang Zhang, Hongxia Yan & Hongen Jia

Adv. Appl. Math. Mech., 8 (2016), pp. 386-398.

Published online: 2018-05

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  • Abstract

In this paper, we study a new stabilized method based on the local pressure projection to solve the semi-linear elliptic equation. The proposed scheme combines nonconforming finite element pairs NCP1−P1triangle element and two-level method, which has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, but have more favorable stability and less support sets. Stability analysis and error estimates have been done. Finally, numerical experiments to check estimates are presented.

  • Keywords

Semi-linear elliptic equations, two-level method, nonconforming finite element method, stabilized method.

  • AMS Subject Headings

35Q30, 74S05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-386, author = {}, title = {A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {386--398}, abstract = {

In this paper, we study a new stabilized method based on the local pressure projection to solve the semi-linear elliptic equation. The proposed scheme combines nonconforming finite element pairs NCP1−P1triangle element and two-level method, which has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, but have more favorable stability and less support sets. Stability analysis and error estimates have been done. Finally, numerical experiments to check estimates are presented.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m842}, url = {http://global-sci.org/intro/article_detail/aamm/12094.html} }
TY - JOUR T1 - A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 386 EP - 398 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m842 UR - https://global-sci.org/intro/article_detail/aamm/12094.html KW - Semi-linear elliptic equations, two-level method, nonconforming finite element method, stabilized method. AB -

In this paper, we study a new stabilized method based on the local pressure projection to solve the semi-linear elliptic equation. The proposed scheme combines nonconforming finite element pairs NCP1−P1triangle element and two-level method, which has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, but have more favorable stability and less support sets. Stability analysis and error estimates have been done. Finally, numerical experiments to check estimates are presented.

Sufang Zhang, Hongxia Yan & Hongen Jia. (2020). A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations. Advances in Applied Mathematics and Mechanics. 8 (3). 386-398. doi:10.4208/aamm.2014.m842
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