TL;DR
This paper proves the uniform spatial convergence of the Jordan-Kinderlehrer-Otto scheme for linear parabolic equations on the flat torus, advancing the understanding of its numerical stability and accuracy.
Contribution
It establishes the first rigorous proof of uniform convergence for the scheme in this setting, filling a gap in the theoretical analysis.
Findings
Proves uniform convergence of the scheme
Validates the scheme's stability for linear parabolic equations
Provides theoretical foundation for numerical methods on the torus
Abstract
In this paper, we prove that the Jordan-Kinderlehrer-Otto scheme for a family of linear parabolic equations on the flat torus converges uniformly in space.
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