Finite Element Methods for Flow Problems

Preface. 1. Introduction and preliminaries. Finite elements in fluid dynamics. Subjects covered. Kinematical descriptions of the flow field. The basic conservation equations. Basic ingredients of the finite element method. 2. Steady transport problems. Problem statement. Galerkin approximation. Early Petrov-Galerkin methods. Stabilization techniques. Other stabilization techniques and new trends. Applications and solved exercises. 3. Unsteady convective transport. Introduction. Problem statement. The methods of characteristics. Classical time and space discretization techniques. Stability and accuracy analysis. Taylor-Galerkin Methods. An introduction to monotonicity-preserving schemes. Least-squares-based…