The College of Science in the Department of Mathematics discussed a Ph.D. thesis entitled "Numerical Study Of Inelastic Fluid Flow In Contraction Geometry By Using A Taylor- Galerkin Pressure - Correction Finite Element Method" by postgraduate student Alaa Abdul Wahed Sharhan. The objective of the thesis is to perform a numerical simulation of Newtonian and non-Newtonian (inelastic) fluids in contraction (4:1, 6:1, and 8:1) based on the Taylor-Gallerkin pressure-corrected finite element method (TGPC-FEM).