The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation {△^2u ＋ a（x）u = g（x, u）u∈ H^2（R^N）, where the condition u∈ H^2（R^N） plays the role o...The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation {△^2u ＋ a（x）u = g（x, u）u∈ H^2（R^N）, where the condition u∈ H^2（R^N） plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.展开更多
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 matchi...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.展开更多
基金Supported by the National Natural Science Foundation of China (10631030)PHD specialized grant of Ministry of Education of China (20060511001) and supported in part by the Xiao-Xiang Special Fund, Hunan
文摘The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation {△^2u ＋ a（x）u = g（x, u）u∈ H^2（R^N）, where the condition u∈ H^2（R^N） plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.
基金This work was subsidized by the special funds for major state basic research projects under 2005CB321700 and a grant from the National Science Foundation （NSF） of China （No. 10471144）.
文摘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.
