AI & ML
Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow
arXiv cs.NA0 views
arXiv:2610.32588v1 Announce Type: new Abstract: We study the stochastic harmonic map heat flow into the sphere driven by a Stratonovich noise term that formally preserves the spherical constraint by construction. Starting from a fully discrete, implementable numerical scheme, we prove its convergence to the novel solution concept of probabilistically strong, analytically energy-variational solutions. This yields the first existence result for probabilistically strong solutions in the three-dimensional setting on the prescribed stochastic basis. In addition, we establish weak-strong uniqueness and illustrate our theoretical findings with numerical experiments.
Source:https://arxiv.org/abs/2610.32588PreviousA linear dual-field finite element method for incompressible MHD, part I: cross-helicity and Alfv\'enic alignment in periodic domainsNextUniversal neural network approximation of symmetric polyconvex energies and envelopes
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