In this paper, three a posteriori error estimators of the error in the semidiscrete finite element solution (discrete in space arid continuous in time) of parabolic partial differential equations are analyzed. This approach is based on a posteriori error estimators for the elliptic PDEs. It is proven that guaranteed (resp. asymptotically exact) a posteriori error estimator for the elliptic problem yields the guaranteed (resp. asymptotically exact) estimator for the parabolic problem.
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