THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION

The mortar element method is a new domain decomposition method(DDM)with nonover- lapping subdomains.It can handle the situation where the mesh on different subdomains need not align across interfaces,and the matching of discretizations on adjacent subdo- mains 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 assump- tion.