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Abstract
Introduction to programming the Finite Element Method (FEM) in 1D and 2D.
Objective
Topics covered include thermal diffusion, elasticity, Stokes flow, isoparametric elements, and code verification using the method of manufactured solutions. The focus is on hands-on programming, and you will learn how to write FEM codes starting with an empty Julia or Python script.
Content
Course content includes brief derivation and implementation details for the Finite Element Method (FEM) for thermal diffusion, linear elasticity, and incompressible Stokes flow, using numerical quadrature and isoparametric elements. 1-dimensional examples are extended to 2 dimensions. Code verification is introduced, using the method of manufactured solutions. The focus is on hands-on programming; course exercises encourage development of a series of increasingly-complex codes, starting with an empty Julia or Python script. A final project allows students flexibility to apply the method to an application of interest or to a standard problem.
Resources
Lecture Notes
The script will be made available online.
Literature
There is no mandatory literature. Some recommended literature will be discussed and made available during the course.