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.
A class of nonlinear parabolic equation on a polygonal domain Ω belong to R^2 is investigated 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.
基金
Supported by the Natural Science Foundation of Hunan under Grant No. 06C713.
关键词
抛物线方程
有限元分析
多角形域
匹配
偏微分方程
Nonlinear parabolic equation
finite element method
overlapping non-matching grids
partition of unity.
