Finite Element Methods 1 (NMNV405) — Practicals (Winter Semester 2022/2023)
This class will provide exercises to explore the finite element method.
Practicals
Monday 14:00 – 15:30, K5 Sokolovská 83 Karlín
Homework
There will be four homeworks during the course of the year. Obtaining credit for this course will involve obtaining at least 50% of the marks available from these homeworks.
Basis Functions
Examples of various basis functions on triangles and rectanges can be found here.
The displayed basis function can be changed via the selection boxes in the top left corner. The bottom left corner allows switching the view between 3D (orthogonal and perspective) and 2D views. In 3D view the basis function can be rotated by dragging. In the bottom left corner the principal lattice (white lines) can be toggled on/off.
The following website also lists details about all the basis functions we have discussed (plus a lot more): defelement.com
Notes on Gaussian Quadrature
The following journal article has information on the choice of points and weights for Gaussian quadrature on a triangle:
Dunavant, D.A. (1985), High degree efficient symmetrical Gaussian quadrature rules for the triangle. Int. J. Numer. Meth. Engng., 21:1129-1148. https://doi.org/10.1002/nme.1620210612
Example FEM Code
An example MATLAB finite element code which solves the problem
-Δu = f,
on the unit square [0, 1]2 with forcing function
f = 2π2 sin πx sin πy,
and homogeneous Dirichlet boundary conditions is available in the following zip file:
The main source is contained in fem.m.