Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations

2022/01/16 by Zhao, Chengchao, Liu, Nan, Ma, Yuheng +1
#65M06 #65M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2201.06008

Abstract

In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is constructed by using the variable time-step BDF2 for the linear term and a Newton linearized method for the nonlinear term in time combining with a Galerkin finite element method (FEM) in space. We prove the unconditionally optimal error estimate of the proposed scheme under mild restrictions on the ratio of adjacent time-steps, i.e. 0

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