| Abstract: |
| In this talk, we propose a new approach for the numerical approximation of (weak) solutions to nonlinear stochastic partial differential equations. Using the stochastic Allen-Cahn equation as a prototype for nonlinear stochastic partial differential equations with multiplicative noise, we present an augmented version of the scalar auxiliary variable technique that provides an unconditionally energy stable, fully discrete finite element scheme that is linear with respect to the unknown quantities. By recovering a discrete version of the energy estimate and establishing Nikolskii estimates with respect to time we are able to prove convergence of appropriate subsequences of discrete solutions towards martingale solutions by applying Skorokhod-type arguments and the martingale representation theorem. |
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