Introduction to Finite Element Methods

CEE 361 / MAE 325 / MSE 331 /CEE 513

Logistics

Lectures: TTh 11:00am-12:20pm, Friend Center 008
Precepts: M 7:30pm-8:20pm, Friend Center 110

Instructor: Maurizio M. Chiaramonte
Email: chiaramonte at princeton.edu
Office hours: W 1:00pm - 3:00pm, E324

Assistant Instructor: Vivek Kumar
Email: vivekk at princeton.edu
Office hours: M 8:20pm-10:20pm, Friend Center 110

News

Upcoming Events

  • [Nov 7, 2017] Project proposal due

  • [Oct 26, 2017] Mid-term exam in Friend 008 from 11:00am to 12:20pm.

  • [Sept 14, 2017] Welcome to Introduction to Finite Element Methods’ first class!

Course Overview

The course introduces fundamental concepts and technologies of primal finite element methods for linear elliptic boundary value problems. The course covers an overview of finite element methods for a one-dimensional model problem including the weak, Galerkin and matrix forms, error analysis and superconvergence. The direct stiffness method of structural analysis is introduced to present the notion of assembly. Extension of the finite element to multiple dimensions are carried out, first for second order scalar valued equations, such as the heat equation and Darcy's flow in porous materials, and later extended to vector valued equations such as the elasticity equations. The course then concludes with the C0 approach to plates and beams and contrasts it with matrix structural analysis approaches. The element formulations and data structures, isoparametric interpolations, locking issues, analysis of errors and convergence of approximations, as well as treatment of constraints and variational crimes will all be discussed.

In the course we will use python for computing assignments and we will also use the high-level finite element toolkit FEniCS to explore properties of finite element methods and build simulations.

Syllabus