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 - <p style="text-align: justify;">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. &nbsp;</p>