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A posteriori error estimates in the maximum norm for parabolic problems. (English) Zbl 1196.65153
The authors present a posteriori error estimates for the approximate solution of the parabolic partial differential equation. A posteriori bounds in the maximum norm for semidiscrete finite element approximations is derived using the elliptic reconstruction technique of the third author and R. H. Nochetto [SIAM J. Numer. Anal. 41, No. 4, 1585–1594 (2003; Zbl 1052.65088)] and heat kernel estimates for linear parabolic problems. The time domain is discretised by the backward Euler method and follows the elliptic reconstruction for the fully discrete problems. A number of lemmas and theorem are derived for existence and uniqueness of the problem. It is desired to present some numerical experiments to illustrate the method.

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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