Nonsmooth data error estimates for fully discrete finite element approximations of semilinear parabolic equations in Banach space

Implicit-explicit (IMEX) Euler formula together with finite element methods is proposed to solve numerically rather general semilinear parabolic differential equations with initial data in Banach space...., 0 <.. = 1. The time-space regularity of solutions to this class of equations is first investigated. Stability and error estimates are provided for this fully discrete scheme by discrete semigroup method. In the special case when.. is the Hilbert space..2(..), these error estimates bridge the gap between the existing results on this scheme for semilinear parabolic problems with initial data in..2(..) and in.. 1(..) under general nonlinearity. Numerical experiments for nonlinear Allen-Cahn equations verify and complement our theoretical results.