Please use this identifier to cite or link to this item:
Title: Maximal L-p error analysis of fems for nonlinear parabolic equations with nonsmooth coefficients
Authors: Li, BY 
Sun, WW
Keywords: Finite element method
Nonlinear parabolic equation
Nonsmooth coefficients
Maximal L-P-regularity
Optimal error estimate
Issue Date: 2017
Publisher: Institute for Scientific Computing and Information
Source: International journal of numerical analysis and modeling, 2017, v. 14, no. 4-5, p. 670-687 How to cite?
Journal: International journal of numerical analysis and modeling 
Abstract: The paper is concerned with L-P error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron with a nonlinear and Lipschitz continuous diffusion coefficient. We first establish the discrete maximal L-P-regularity for a linear parabolic equation with time-dependent diffusion coefficients in L-infinity(0, T; W-1,W-N+epsilon) boolean AND C((Omega) over bar x [0, T]) for some epsilon > 0, where N denotes the dimension of the domain, while previous analyses were restricted to the problem with certain stronger regularity assumption. With the proved discrete maximal L-P-regularity, we then establish an optimal L-P error estimate and an almost optimal L-infinity error estimate of the finite element solution for the nonlinear parabolic equation.
ISSN: 1705-5105
Appears in Collections:Journal/Magazine Article

View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

Citations as of Mar 19, 2018

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.