Constructive error analysis of a full-discrete finite element method for the heat equation
For researchers in numerical analysis, this provides a verified computational framework for error bounds in heat equation discretizations, though it is an incremental extension of prior work.
The paper extends constructive error estimates to a full-discrete finite element method for the heat equation, proving numerical stability via verified computations. The method is simpler to implement than previous approaches.
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.