:Spring 2014: Math 610-Lab (Numerical Methods for PDEs)

• Announcements

• 1. Format for the report of programming assignment
* Your report should be a PDF file looking like this: report.pdf.
- Here is the LaTeX source used to create this PDF file : report.tex, graph.ps
* To produce a .DVI file from your .TEX file, use the command: latex [name_of_file].tex
* To convert your .DVI file to a .PS/.PDF file use the commands dvips or dvipdf.

• In Class Materials
1. [Jan.22] 2D finite elements. Generating the mesh.
• A good mesh generator: Triangle
• Reference input data (basic.poly) : Square
• Command: ./triangle(./triangle -o1 -a.064 -q30 square.poly), ./showme

2. [Jan.29] Programming Assignment I - Exercise 1. is due on next week. (Feb.5th)
** Things to submit in the report. **
• Check your implementation by picking a certain solution, verify it's second order
• Matrix and Right hand side vetor for the case h=1/3
• Plot Solution for #1 and #2 with u(0)=u(1)=1
• Plot Solution for #1 and #2 with u(0)=u'(1)=0
• Plot loglog graph for h vs error for each problem.

3. [Feb.5] Programming Assignment I - Exercise #2(1-3 only). is due on next week. (Feb.12th)
** Reminder. **
• Define linear basis functions
• Use Gaussian Quadrature rule with 3 points for the integration.
• Build local/global mass/stiffness matirces
• Don't forget lifting for Dirchilet boundary condition if it's necessary
• Calculate L_infty,L2, and H1 error

** Things to submit in the report. **
• Plot the solutions for each problem.
• Plot loglog graph for h vs error(each norm) for each problem.

4. [Feb.12] FINAL DUE: Programming Assignment I is due on next week. (Feb.17th)
** We might loose order on Exercise #2-4 **
• Plot the solutions for each problem.
• Plot loglog graph for h vs error(each norm) for each problem.