The talk will elaborate on the formulation of the stochastic partial differential equations of elliptic type and on the obtaining the needed data from experiments. It will address the equations with stochastic coefficients and right hand side. The problem is transformed into deterministic problem in a high dimensional space.The adaptivity then includes dimensional reduction, shape functions (mesh) selection as well selection of the combination of various solution methods.This is in possible conjunction with the obtaining data from the experiments.