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Volume 23, Issue 5
The Mortar Element Method for a Nonlinear Biharmonic Equation

Zhong-Ci Shi & Xue-Jun Xu

J. Comp. Math., 23 (2005), pp. 537-560.

Published online: 2005-10

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  • Abstract

The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and $H^1$-norm estimates are obtained under a reasonable elliptic regularity assumption.  

  • Keywords

Mortar method, Nonlinear biharmonic equation, $H^1$-norm error, Energy norm error.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-537, author = {Zhong-Ci Shi and Xue-Jun Xu}, title = {The Mortar Element Method for a Nonlinear Biharmonic Equation}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {5}, pages = {537--560}, abstract = {

The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and $H^1$-norm estimates are obtained under a reasonable elliptic regularity assumption.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8838.html} }
TY - JOUR T1 - The Mortar Element Method for a Nonlinear Biharmonic Equation AU - Zhong-Ci Shi & Xue-Jun Xu JO - Journal of Computational Mathematics VL - 5 SP - 537 EP - 560 PY - 2005 DA - 2005/10 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8838.html KW - Mortar method, Nonlinear biharmonic equation, $H^1$-norm error, Energy norm error. AB -

The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and $H^1$-norm estimates are obtained under a reasonable elliptic regularity assumption.  

Zhong-Ci Shi and Xue-Jun Xu. (2005). The Mortar Element Method for a Nonlinear Biharmonic Equation. Journal of Computational Mathematics. 23 (5). 537-560. doi:
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