St. Metzger (FAU Erlangen-Nürnberg)
<p>
  The scalar auxiliary variable (SAV) method was originally introduced in [Shen,
  Xu, Yang, J. Comput. Phys., 2018] for the discretization of deterministic
  gradient flows. By introducing an additional scalar variable, they were able
  to formulate linear numerical schemes that are still unconditionally stable
  with respect to a modified energy.
  This talk addresses the application of the SAV method to nonlinear stochastic
  partial differential equations with multiplicative noise. Using the stochastic
  Allen-Cahn equation as a prototype, we motivate why a straightforward
  application of the SAV method will not provide satisfactory results and
  present an augmented SAV method that remedies the shortcomings and allows for
  a rigorous convergence proof. Using a discrete version of the energy estimate
  as a starting point, we are able to show convergence towards pathwise unique
  martingale solutions by applying Jakubowski's generalization of Skorokhod's
  theorem. Convergence towards (stochastically) strong solutions can then be
  shown using a generalization of the Gyöngy-Krylov characterization of
  convergence in probability.
  We conclude by presenting numerical simulations which underline the
  practicality of the scheme and the importance of the introduced augmentation.