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Title: Maximal Lp error analysis of fems for nonlinear parabolic equations with nonsmooth coefficients
Authors: Li, B 
Sun, W
Keywords: Finite element method
Maximal Lp -regularity
Nonlinear parabolic equation
Nonsmooth coefficients
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 Lp 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 Lp -regularity for a linear parabolic equation with time-dependent diffusion coefficients in L∞(0, TMergeCell W1,N+ϵ) ∩ C(Ω × [0, T ]) for some ϵ >MergeCell 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 Lp -regularity, we then establish an optimal Lp error estimate and an almost optimal L∞ error estimate of the finite element solution for the nonlinear parabolic equation.
ISSN: 1705-5105
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