The long-time behavior of finite-element approximations of solutions of semilinear parabolic problems

Error estimates for finite-element approximations of the solutions to semilinear parabolic problems are proved. Under the hypothesis that the exact solution is asymptotically stable as $t \to \infty $, error estimates of optimal order that hold uniformly on the unbounded time interval $0 \leqq t < \infty $ are obtained. Both semidiscrete and completely discrete approximations are considered.