FEM_2011
Finite Element Seminar
Fall, 2011

http://people.sc.fsu.edu/~jburkardt/classes/fem_2011/fem_2011.html

FEM_2011 is the home page for the class ISC5939-4, "The Finite Element Method", a seminar offered by the Department of Scientific Computing at Florida State University, Fall Session 2011.

• 2011_09_02.html, class notes for September 2.

For the class on October 7, 2011, Miro Stoyanov wrote a program to illustrate the spectral finite element method for a particular example. He made a symbolic version, which requires MATLAB's symbolic toolbox, and a numerical version, which estimates the integrals using MATLAB's quad() function:

• solveFEM_numeric.m, a MATLAB program for the spectral finite element method, which uses numerical integration to evaluate the necessary integrals, in order to solve the problem: uxx = - pi^2 * sin(pi*x), u(-1) = u(1) = 0, using the family of basis polynomials phi_i(x) = x^(i-1) * (x+1)(x-1).
• solveFEM_symbolic.m, a MATLAB program for the spectral finite element method, which uses MATLAB's Symbolic Toolbox to evaluate the necessary integrals, in order to solve the problem: uxx = - pi^2 * sin(pi*x), u(-1) = u(1) = 0, using the family of basis polynomials phi_i(x) = x^(i-1) * (x+1)(x-1).

For the class on October 14, 2011, Miro Stoyanov prepared a program which uses piecewise linear elements to solve a 1D finite element problem. He has corrected the error computation.

• solveFEM_assign2.m, the MATLAB program.

For the class on October 21, 2011, Miro Stoyanov prepared two program which solve a finite element problem on a uniform or nonuniform mesh:

• solveFEM_assign3_uniform.m, the MATLAB program for the uniform mesh.
• solveFEM_assign3_nonuniform.m, the MATLAB program for the nonuniform mesh.

For the class on October 21, 2011, Miro Stoyanov discussed the GMRES algorithm. A bit of background on this algorithm is available in gmres.pdf.

For the class on October 28, 2011, Miro Stoyanov prepared two programs which solve the Assignment 4 problem. One program is standalone, the other requires SuiteSparse, BLAS and LAPACK. The complete set of files is available in one ZIP file.

• Assignment4.zip
• plotSolution.m, a MATLAB program to plot the solution.

For the class on November 4, 2011, John Burkardt presented a discussion of meshing for finite element problems.

• fem_meshing.pdf
  slides for the talk on finite element meshing.
• ../../m_src/fem_meshing/fem_meshing.html
  a directory of example data files, and short codes in MATLAB, C++ and FORTRAN, for displaying, writing and reading mesh files.
• ../../m_src/distmesh/distmesh.html
  information about the MATLAB DISTMESH meshing code.
• ../../m_src/mesh2d/mesh2d.html
  information about the MATLAB MESH2D meshing code.
• ../../c_src/triangle/triangle.html
  information about the C TRIANGLE meshing code.

There was no class on November 11!

Typically, the departmental preliminary exam includes one question about the finite element method. For the class on November 18, Xi Chen talked about these questions and will demonstrate what a reasonable answer to such a question looks like.

• prelim_fem.pdf, questions about the finite element method from past years.
• prelim_fem_answer.pdf
  suggested answers for the old questions.

There will be no class on November 25!

For the class on December 2, 2011, John Burkardt presented a discussion of finite element methods for the Stokes equations of fluid flow.

• fem_stokes.pdf
  slides for the talk on finite element methods for the Stokes equations.

Chapters from "Finite Element Methods" by Gunzburger and Peterson:

• chapter1.pdf, chapter 1.
• chapter2.pdf, chapter 2.
• chapter3.pdf, chapter 3.
• chapter4.pdf, chapter 4.
• chapter5.pdf, chapter 5.
• chapter6.pdf, chapter 6.

Finite Element Treatment of the Navier Stokes Equations:

• fem_ns1.pdf, discusses the Navier-Stokes equations;
• fem_ns2.pdf, discusses the setup of the finite element geometry and basis functions;
• fem_ns3.pdf, discusses the Stokes equations;
• fem_ns4.pdf, discusses the Navier-Stokes equations;
• fem_ns5.pdf, is material that I have not organized yet;
• fem_ns6.pdf, is a draft of a discussion of the computation and use of a compressed column sparse matrix format for the jacobian.