EGM 6352 - ADVANCED FINITE ELEMENT METHODS
Fall 1998
Catalog Description: Prerequisite: Consent of instructor. Advanced topics on classical FEM. Non-classical FEM (discontinuous Galerkin methods, nonconforming/mixed FEM, etc.). Transient problems. Optimization theory applied to mixed FEM; incompressible flows. Generalized Hu-Washizu mixed variational principle. Electromagnetics, heat, fluids, solids. Other advanced topics (e.g., edge elements, element-free Galerkin method, etc.)
Textbook: None required.
References:
Many other references are listed in the
Detailed Course Contents
(Postscript, 136KB).
(For those of you who cannot read or download PostScript documents from
my web page, see my note at the bottom of this web page.)
Prerequisites by topics: EGM 6351 Finite Element Methods, or consent of the instructor. Undergraduate courses on linear algebra.
Goals: To provide a solid foundation for the classical FEM, its applications in all areas of engineering, and to treat advanced concepts of non-classical FEM, e.g., discontinuous Galerkin method, mixed FEM, founded on solid mathematical setting. A follow-up course after EGM 6351, this course is designed to sharpen (i) the basic concepts of the FEM, and (ii) the skills to formulate FE solution to solve the PDE's governing physical phenomena. Various types of PDE's are addresses, including hyperbolic PDE's in flow problems. The course prepares engineering students to access the rich mathematics literature on the subject. Further, this course provides an introduction to nonlinear FEM, which is taught in detail in the Nonlinear FEM course in Spring 1999.
Topics: Classical FE formulation: Poisson equation in R^n, biharmonic equation, elastodynamic equations, Maxwell equations in electromagnetics. Classical FEM as a projection method. FE function spaces: Lagrange elements of various types in R^n, Hermite elements with various types, elements for plate problems (biharmonic equation), etc., mathematical properties. Discontinuous FEM for transient problems: space-time FEM. Problems with differential constraint (e.g., incompressible flow, etc.), mixed FEM. Optimization theory and its application to mixed FEM. Application of mixed FEM to electromagnetics: Edge elements. Navier-Stokes equations, convection-dominated flow problems: Upwind-Petrov Galerkin method, etc. Introductory nonlinear FEM. And more...
Project: To be announced in class.
Computer support required: Access to a computer.
Engineering applications: Electromagnetics, heat, fluid and solid mechanics.