The finite element method: discretization and application to heat convection problems

In this chapter, we give an overviewof the finite element method and its applications to heat and fluid flow problems. An introduction to weighted residual approximation and finite element method for heat and fluid flow equations are presented. The characteristic–based split (CBS) algorithm is also presented for solving the incompressible thermal flow equations. The algorithm is based on the temporal discretization along the characteristics, and the high-order stabilization terms appear naturally from this kind of discretization. The artificial compressibility (AC) and the semi-implicit (SI) versions of the CBS scheme are presented and some examples are also given to demonstrate the main features of both the schemes.