We augment a thermodynamically consistent diffuse interface model for the description of line tension phenomena by multiplicative stochastic noise to capture the effects of thermal fluctuations and establish the existence of pathwise unique (stochastically) strong solutions. By starting from a fully discrete linear finite element scheme, we do not only prove the well-posedness of the model, but also provide a practicable and convergent scheme for its numerical treatment. Conceptually, our discrete scheme relies on a recently developed augmentation of the scalar auxiliary variable approach, which reduces the requirements on the time regularity of the solution. By showing that fully discrete solutions to this scheme satisfy an energy estimate, we obtain first uniform regularity results. Establishing Nikolskii estimates with respect to time, we are able to show convergence towards pathwise unique martingale solutions by applying Jakubowski's generalization of Skorokhod's theorem. Finally, a generalization of the Gy\"ongy--Krylov characterization of convergence in probability provides convergence towards strong solutions and thereby completes the proof.

翻译：我们通过引入乘性随机噪声来增强描述线张力现象的热力学一致扩散界面模型，以捕捉热涨落效应，并证明了路径唯一（随机）强解的存在性。从完全离散的线性有限元格式出发，我们不仅证明了模型的适定性，还为其数值处理提供了一种实用且收敛的格式。从概念上讲，我们的离散格式依赖于最近发展的标量辅助变量方法的增强形式，该形式降低了对解的时间正则性要求。通过证明该格式的完全离散解满足能量估计，我们获得了首项一致正则性结果。通过建立关于时间的尼科尔斯基估计，我们能够应用雅库博夫斯基对斯科罗霍德定理的推广，证明其向路径唯一鞅解的收敛性。最后，对Gyöngy-Krylov概率收敛特征的推广实现了向强解的收敛，从而完成了证明。