Abstract: The Poisson equation is dealt with in three dimensional domains of revolution using the newly developed semi analytical method,the finite element method of lines(FEMOL).The original problem has been converted,by means of the Fourier expansion in circular direction,into a series of two dimensional problems defined on the plane of revolution.Corresponding FEMOL elements have been constructed.The singularities at r=0 in the cylindrical coordinates and on degenerate element sides or lines have reasonably been dealt with in details.Numerical results are given and show that this method is able to produce highly accurate and reliable solution with few elements.

Key words: Finite Element Method of Lines, Poisson equation, three-dimensional domain of revolution