  Classical approximation results for stochastic differential equations analyze
the $L^p$-distance between the exact solution and its Euler-Maruyama
approximations. In this article we measure the error with temporal-spatial
H\"older-norms. Our motivation for this are multigrid approximations of the
exact solution viewed as a function of the starting point. We establish the
classical strong convergence rate $0.5$ with respect to temporal-spatial
H\"older-norms if the coefficient functions have bounded derivatives of first
and second order.
