Numerical Solution of the Compressible Boundary-Layer Equations Using the Finite Element Method

We study the application of the finite element method (FEM) to the boundary-layer equations governing both incompressible (with heat transfer) and compressible fluids in two dimensions. Numerical solutions for this set of equations have traditionally been obtained using the finite difference method (FDM), where the derivatives are approximated by difference quotients resulting in an algebraic representation of the partial differential equations. In FEM, the flow region is subdivided into a number of small regions called finite elements, and the dependent variables are interpolated within each element by functions of compatible order