ERROR ESTIMATES FOR TWO-SCALE COMPOSITE FINITE ELEMENT APPROXIMATIONS OF NONLINEAR PARABOLIC EQUATIONS  

作　　者：Tamal Pramanick 

机构地区：[1]Department of Mathematics,National Institute of Technology Calicut,Kozhikode-673601,India

出　　处：《Journal of Computational Mathematics》2021年第4期493-517,共25页计算数学（英文）

基　　金：The author gratefully acknowledges valuable support provided by the Department of Mathematics,NIT Calicut and the DST,Government of India,for providing support to carry out this work under the scheme TIST(No.SR/FST/MS-I/2019/40).

摘　　要：We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.

关 键 词：Composite nite elements Nonlinear parabolic problems Coarse-scale Finescale Semidiscrete Fully discrete Error estimate 

分 类 号：O241.82[理学—计算数学]