Partition of Unity for a Class of Nonlinear Parabolic Equation on Overlapping Non-Matching Grids

摘要

A class of nonlinear parabolic equation on a polygonal domain Ω  R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, 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 theoretical results is also given.