  This paper studies the convergence of a spatial semi-discretization for a
backward semilinear stochastic parabolic equation. The filtration is general,
and the spatial semi-discretization uses the standard continuous piecewise
linear element method. Firstly, higher regularity of the solution to the
continuous equation is derived. Secondly, the first-order spatial accuracy is
derived for the spatial semi-discretization. Thirdly, an application of the
theoretical result to a stochastic linear quadratic control problem is
presented.
