Title: Dimension Splitting Algorithm for 3-D Problem

Abstract: In this talk, a so-called finite element dimension splitting
algorithm (DSA) for a three dimensional elliptic equation in a cubic
domain is discussed. The main idea of DSA is that, within certain
proper finite element subspace, the 3-D elliptic equation can be
approximated by a series of coupled 2-D elliptic equations defined in
X-Y plane along Z direction. Then an iterative algorithms consisting
of solving this series of 2-D problems is given and the convergence
speed of the iterative algorithm and the error estimation of the
approximate solution are investigated. The analysis shows that the
convergence speed of DSA for 3-D elliptic equation depends heavily on
mesh scale along Z direction.  Based on the analysis results, a
possible strategy of acceleration is briefly discussed.