Abstract. This paper is concerned with the design and implementation of efficient solution algorithms for elliptic PDE problems with correlated random data. The energy orthogonality that is built into stochastic Galerkin approximations is cleverly exploited to give an innovative energy error estimation strategy that utilizes the tensor product structure of the approximation space. An associated error estimator is constructed and shown theoretically and numerically to be an effective mechanism for driving an adaptive refinement process. The codes used in the numerical studies are available online.Key words. stochastic Galerkin methods, stochastic finite elements, PDEs with random data, error estimation, a posteriori error analysis, adaptive methods, parametric operator equations AMS subject classifications. 35R60, 65C20, 65N30, 65N15.1. Introduction. Stochastic Galerkin approximation methods have emerged over the last decade as an efficient alternative to sampling methods for computing solutions (and associated quantities of interest) when studying linear elliptic PDE problems with correlated random data. A typical strategy is to combine conventional (h-) finite element approximation on the spatial domain with spectral (p-) approximation on a finite-dimensional manifold in the (stochastic) parameter domain. [5]. The strategy that is developed herein is similar in spirit to that developed by Eigel et al. [7], but it is novel in that a posteriori estimates of the error reduction in the energy norm (rather than the error itself) are used to guide the adaptivity process.An outline of the paper is as follows. Sections 2 and 3 set the problem of interest within the general framework of parametric operator equations with a potentially infinite-dimensional parameter space. The new error estimator is identified in Section 4. The estimator is shown to be reliable and efficient, and its properties are established that prove useful when individual error components are used to drive adaptive refinement. A specific implementation of an adaptive refinement strategy is described in section 5, and a set of numerical experiments that illustrate the effectiveness of the strategy is presented in section 6. One notable feature is that our software implementation is not limited to the lowest-order conforming spatial approximationthis means that we can solve spatially-regular problems to high accuracy with just a few adaptive refinement steps.