• Instructor : Dr. L. Vu-Quoc
• Classroom: 327 Aero Bldg
• Class time:

Tue, period 8 (3:00pm - 3:50pm)
Thu, periods 8+9 (3:00pm - 4:55pm)
• Office hours:

Tue, period 7 (1:55-2:45) and period 9 (4:05-4:55)
Thu, period 7 (1:55-2:45)

Textbook: None required.

References:

• The book by T.J.R. Hughes [1987], The Finite Element Method, Prentice Hall, is a good reference.
• In previous years, I used several references listed in the Detailed Course Contents ( ps, pdf)
• This year, I will hand out new journal articles, and indicate new books that can be used as references for the course. In addition, I will constantly update the detailed course contents for this year.

Prerequisites by topics: A course on the FEM. Undergraduate 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 a complement to the course 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 addressed, 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, depending on the mutual interest between students and instructor.

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... The selection of the topics to be lectured depends on the mutual interest between the students and the instructor.

Project: To be announced in class.

Computer support required: Access to a computer (e.g., a PC).

Engineering applications: Electromagnetics, heat, fluid and solid mechanics.

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