In this paper, we present a new full-discrete finite element method for the heat equation, and show the numerical stability of the method by verified computations. Since, in the error analysis, we use the constructive error estimates proposed ny Nakao et. all in 2013, this work is considered as an extention of that paper. We emphasize that concerned scheme seems to be a quite normal Galerkin method and easy to implement for evolutionary equations comparing with previous one. In the constructive error estimates, we effectively use the numerical computations with guaranteed accuracy.
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