We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.

中文翻译：

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自适应随机搭配与有限元的收敛

我们考虑具有随机扩散参数的椭圆偏微分方程，该参数通过参数域中的随机搭配方法和空间域中的有限元方法离散化。我们首次证明了随机搭配算法的收敛性，该算法自适应地丰富了参数空间并细化了有限元网格。