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Markos A. Katsoulakis, Georgios T. Kossioris, Omar LakkisA Finite Element Method Via Noise Regularization for the Stochasitc Allen-Cahn ProblemWe study finite element approximations of stochastic partial differential equations of Ginzburg-Landau type and the main paradigm considered in this paper is the stochastic Allen-Cahn model. We first demonstrate that the constructed stochastic finite element approximations are within an arbitrary level of tolerance from the corresponding one-dimensional stochastic partial differential equation; secondly we show that the finite element approximation is close to the most probable deterministic tra jectory of the stochastic Allen-Cahn equation, even in large time intervals where interfaces form and evolve according to macroscopic mean curvature-dependent evolutions.Bibliographical note: |