Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting. Extensions to other variants of adaptive collocation methods (including the classical one proposed in the paper "Dimension-adaptive tensor-product quadratuture" Computing (2003) by T. Gerstner and M. Griebel) is explored.

翻译：显示固定参数扩散方程式的适应性同位法与有限维度等离子系数的趋同性。适应性算法依赖于最近推出的基于残余的可靠后继误差估计器。关于趋同证据,最近用于具有等级误差估计器的随机加热金法的战略被转移到同位地点设置。探索了适应性同位法的其他变体(包括T. Gerstner和M. Griebel在“Dimension-adoptive Damor-product-Econtature ”的论文中提议的古典方法 (2003年) 。