Can somebody tell me some effective method in sovling pressure correction poisson equations by FEM (no matter using Fractional step method or not) in fortran and how can I deal with the boundary conditions (formed in the process of Galerkin method of the poisson equations). Please tell some detailed referrences. Thank you very much.

I have made the equations but I need some effctive method to solve them. I have tried to use LU decomposition method to solve the matrix of poisson corrction equations in FEM. but I can not get the right answers. so,My question is how can I solve it effectively and how can I deal with the corresbonding boundary conditions form in Galerkin method (Green-Gauss equations)? I have read about relaxition method, but I don't know if it is effcient in FEM?