• Instructor : Dr. L. Vu-Quoc
• Classroom: 327 Aero building
• 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)

Catalog Description: Prerequisite: A course on the FEM, or 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., boundary elements, edge elements, meshfree methods, etc.), depending on mutual interest between students and instructor.

Textbook: None required.

References:

• The book The Finite Element Method (Hughes [2000], Dover Publication), is a good reference. See also my home page for more info on this course as taught in previous years. There will be some significant updates on the course contents depending on mutual interests of students and instructor.
• In previous years, I used several references listed in the Detailed Course Contents (ps, pdf). For Fall 2000, see the detailed course contents.
• This year, I will hand out new journal articles, and indicate new books that can be used as references for the course. Recent research topics such as meshless methods, variational multiscale methods, etc.
  • For meshless methods, I will discuss various meshless methods such as Smoothed Particle Hydrodynamics (SPH) and its corrected variants, the Element-Free Galerkin (EFG) method, and in particular the Meshless Local Petrov-Galerkin (MLPG) method by S. Atluri. Some applications to fracture mechanics may be considered.
  • For variational multiscale methods, I will discuss papers such as The variational multiscale method---A paradigm for computational mechanics by Hughes et al. [1998], etc.
  • Motivation papers:
    • "Chinese will move waters to quench thirst of cities" (New York Times, 27 Aug 02): China's huge civil engineering project; opportunity for computational mechanics?
    • Atomistic mechanisms governing elastic limit and incipient plasticity in crystals, by Li et al., Nature, 2002.
    • Nanoindentation: Measuring material properties at manometer scale.
    • Nanoindentation: Characteristics of silicon
      See also the applications web site of Hysitron, Inc.
    • An adaptive finite-element approach to atomic scale mechanics---the quasicontinuum method,
      Shenoy et al, JMPS, 1999.
  • Other papers will be listed on the course web site as we progress along...
    List of references for Fall 2002. Thu, 31 Oct 2002

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. As 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. For example, the project for a student could consist of reading any recent paper of interest to this student and relevant to the course. On-campus students will make a presentation on her reading of the selected paper; off-campus students will submit a term paper on the selected paper.

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

Other interesting links:

• Science's 10 Most Beautiful Experiments (New York Times, 24 Sep 2002)

[ Bio | Publications | Research | Teaching ]

Home page: Loc Vu-Quoc