CONVERGENCE TO EQUILIBRIUM FOR THE BACKWARD EULER SCHEME AND APPLICATIONS

By Morgan Pierre. 2010

58 citations recorded by the source corpus.

We prove that, under natural assumptions, the solution of the backward Euler scheme applied to a gradient flow converges to an equilibrium, as time goes to infinity. Optimal convergence rates are also obtained. As in the continuous case, the proof relies on the well known Lojasiewicz inequality. We extend these results to the $\theta$-scheme with $\theta\in [1/2, 1]$, and to the semilinear heat equation. Applications to semilinear parabolic equations, such as the Allen-Cahn or Cahn-Hilliard equation, are given

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/00fb0813d6e5f617b4529f204b487dbb16acf32e

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In Applied Mathematics

1. Adam M. Oberman
2. Eitan Tadmor
3. Michael Neilan
4. Susanne C. Brenner

In Computational Mechanics

1. Maxime Laborde
2. Tim Hoheisel
3. Adam M. Oberman

Citations in the corpus

• A regularization interpretation of the proximal point method for weakly convex functions (2020, background): “We do not discuss about the rate of convergence and we refer to [4, 19].”