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We consider a linear elliptic partial differential equation (PDE) with ageneric uniformly bounded parametric coefficient. The solution to this PDEproblem is approximated in the framework of stochastic Galerkin finite elementmethods. We perform a posteriori error analysis of Galerkin approximations andderive a reliable and efficient estimate for the energy error in theseapproximations. Practical versions of this error estimate are discussed andtested numerically for a model problem with non-affine parametricrepresentation of the coefficient. Furthermore, we use the error reductionindicators derived from spatial and parametric error estimators to guide anadaptive solution algorithm for the given parametric PDE problem. Theperformance of the adaptive algorithm is tested numerically for model problemswith two different non-affine parametric representations of the coefficient.

A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case