Advances in Differential Equations and Control Processes
-->
Abstract: In this paper, a class of
nonlinear elliptic problem is discussed on a plane polygonal domain We
propose a finite element method on overlapping non-matching grids for the
nonlinear elliptic problem based on the partition of unity method. The
construction and convergence analysis of a global conforming finite element
method are studied, and we prove that the error of the discrete variational
problem has good approximation properties. Our results are valid for any spatial
dimensions. A numerical example to illustrate the result is also given.
Keywords and phrases: nonlinear elliptic equation, finite element method, overlapping non-matching grids, partition of unity, domain decomposition, convergence analysis.
