论文标题
关于具有仿射扩散的椭圆形部分微分方程的自适应随机搭配的收敛性
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
论文作者
论文摘要
显示了具有有限维仿射系数的固定参数扩散方程的自适应搭配方法的收敛。自适应算法依赖于最近引入的基于剩余的可靠后验误差估计器。为了证明收敛性，将最近用于带有层次误差估计器的随机Galerkin方法的策略转移到搭配设置中。探索了T. Gerstner和M. Griebel的其他自适应搭配方法的扩展（包括“维度自适应张量产物四倍体”计算（2003）中提出的经典一种。
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.
