A posteriori error estimates for the two-step backward differentiation formula method for parabolic equations

摘要

We derive optimal order residual-based a posteriori error estimates for time discretizations by the two-step backward differentiation formula (BDF) method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Eu-ler scheme. Our a posteriori error estimates are of optimal order for the former choice and suboptimal for the latter. Simple numerical experiments illustrate this behavior.