While the FEM was INITIALLY developed to solve diffusion type problems, i.e., stress-strain equations or heat conduction, advances over the past several decades have enabled the FEM to solve advection-dominated problems, INCLUDING incompressible as well as compressible fluid flow. Modifications to the basic PROCEDURE (utilizing forms of upwinding for advection, i.e., Petrov-Galerkin and adaptive meshes) allow general advection-diffusion TRANSPORT equations to be ACCURATELY solved for a wide range of problems.

While the FEM was initially developed to solve diffusion type problems, i.e., stress-strain equations or heat conduction, advances over the past several decades have enabled the FEM to solve advection-dominated problems, including incompressible as well as compressible fluid flow. Modifications to the basic procedure (utilizing forms of upwinding for advection, i.e., Petrov-Galerkin and adaptive meshes) allow general advection-diffusion transport equations to be accurately solved for a wide range of problems.