We proved convergence rates of fully discrete multi-level simultaneous linear collocation approximation of solutions to parametric elliptic PDEs on bounded polygonal domain with log-normal random inputs, based on a finite number of their values at points in the spatial-parametric domain. These convergence rates significantly improve the best-known convergence rates of fully discrete collocation approximation and with some logarithm factors coincide with the convergence rates of best n-term approximation. These results are obtained as consequences of applications to infinite-dimensional holomorphic functions of general results on multi-level linear sampling recovery by extended least squares algorithms in abstract Bochner spaces.
Dũng Đinh (Sun,) studied this question.