Numerical Analysis 3

The finite element method is a widely used numerical method. This course will explain the principles of the method, present the equations relevant to a variety of problems, and provide the keys to implementing the method computationally.

Learn the basics of the finite element method and explore the different types of finite elements (Lagrange, Hermite, Raviart-Thomas, Crouzeix-Raviart). A variety of problems (Laplacian, linear elasticity, Stokes, nonconforming problems) will be addressed and illustrated numerically using scientific software.

The necessary concepts are covered during the first semester of the program.

Recommended prerequisites: Basic programming skills using scientific software.

A sample course schedule is as follows:

1) Review of functional spaces, Lax–Milgram theorem

2) Galerkin method, principles and important theorems (Céa’s lemma, upper infimum condition, Strang’s lemma)

3) One-dimensional finite element method: Lagrange finite elements P1, P2, Pk; Hermite finite elements

4) Higher-dimensional finite element method: Lagrange finite elements P1, Pk, Qk

5) Finite element generation: definitions of the various types of finite elements (Lagrange, Hermite (example of the use of Argyris elements), Crouzeix-Raviart (example of a nonconforming approximation), Raviart-Thomas)

6) The Problem of Linear Elasticity

7) Approximations of Mixed Problems (Laplace and Stokes)

Hourly volumes:

            CM: 24 

            TD: 15

            TP: 7.5

            Land: 0