Numerical methods for stochastic partial differential equations: Analysis of stability and efficiency

This cumulative thesis contains several contributions to the numerical analysis of stochastic partial differential equations. The main focus lies on investigating and improving numerical methods with respect to the qualitative properties stability and efficiency. Here the term stability of a numerical method denotes a measure for the approximation quality of the considered numerical method based on fixed refinement parameters in space and time or on a finite number of independent realisations for Monte Carlo estimators. In contrast, the efficiency of a numerical method for approximating the solution process of SPDEs measures the computational work needed to obtain a certain accuracy. Besides the separate discussion of these two qualitative properties, the emphasis is laid on investigating their interplay and their practical relevance for numerical experiments. This thesis consists of an introductory essay followed by 4 chapters based on 4 scientific articles........