Abstract
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 Euler 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.
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