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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.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
Software:
ALBERTA
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