We derive estimates for a discretization in space of the standard
Cahn–Hilliard equation with a double obstacle free energy.
The derived estimates are robust and efficient, and in practice are combined
with a heuristic time step adaptation.
We present numerical experiments in two and three space dimensions and compare
our method with an existing heuristic spatial mesh adaptation algorithm.
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...
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