拟线性拋物问题有限元全离散格式的渐近展式

Asymptotic Expansions for the Fully Discrete Types of Finite Element Solution of Quaasilinear Parabolic Paroblem

本文在文[4]关于拟线性抛物问题半离散有限元解的渐近展式与外推的基础上,通过讨论全离散解与半离散解之差的渐近展式,得到了拟线性抛物问题的某些全离散格式的渐近展式与外推。

Considering the quasilinear parabolic problem u_t-D_j(a_(ij)(x,t,u)D_iu)+b_i(x,t,u)D_iu=f(x,t,u)(x,t)∈Ω×(0,T) u=0(x,t)∈■Ω×(0,T) u(x,0)=(x)x∈Ω on the basis of the asympansion and extroplation of semidiscrete type of finite element solution,by studying the asymptotic expansion of the difference between the fully discrete and semidiscrete types of solution,we obtain the asymptotic expansions and extrapolations for some fully discrete types of finite element solltion of quasilinear parabolic problem.