SCHEDULE
FEM_2014, Fall Session 2014
Location:
http://people.sc.fsu.edu/~jburkardt/classes/fem_2014/schedule.html
Lectures are in room 468, 2:003:00pm. Problem sessions are held
in 445 DSL (Burkardt) or 456 DSL (van Wyk) or room 468 (seminar room)
as convenient.

Wednesday, 27 August:
Class organization

Monday, 01 September:
Problem Sesssion (Room 445)

Wednesday, 03 September
Lecture: Approximate Solution of a Boundary Value Problem;
a partial differential equation u''=f with boundary conditions.
derivation of the weak form; a discrete space Vh; representation
of the discrete solution as a linear combination of basis functions;
the piecewise linear discrete space; generating the linear system.

Monday, 08 September:
Problem Sesssion (Room 445)

Wednesday, 10 September:
Lecture: the stiffness matrix K and mass matrix M arise from the
variational formulation; how the system matrix A is formed from
K and M; symmetric positive definiteness; K and L and M for the
hat function basis.

Monday, 15 September:
Problem Sesssion (Room 445)

Wednesday, 17 September:
Lecture: the formula for the L matrix; building the linear system
by elements, rather than by nodes; approximating integrals by
quadrature; discussion of the 1D Python program; vector norms;
orthogonality; the error norm; convergence; convergence rates.

Monday, 22 September:
Problem Sesssion (Room 445)

Wednesday, 24 September:
Lecture: the L2 norm, H1 seminorm, and Energy norm;
expected error norm decay rates;
computing a table of values, the L2 norm, the H1 seminorm,
and the average value of the solution;

Monday, 29 September:
Problem Sesssion (Room 445)

Wednesday, 01 October:
Lecture (van Wyk): using FENICS to set up and solve a 1D problem.

Friday, 03 October:
Problem session (Burkardt): on computing the L2 norm and H1 seminorm
of the finite element error.

Monday, 06 October:
Problem Sesssion (Room 445)

Wednesday, 08 October:
Lecture (van Wyk/Burkardt): the finite element interpolant, and its
use in FENICS (and homework); writing a mesh to an XML file, modifying
mesh files by hand to perform refinement, using a mesh that is stored
in a file.

Monday, 13 October:
Problem Sesssion (Room 445)

Wednesday, 15 October:
Welcome visitor Qingguang Guan!
Lecture: the mathematical formulation of elliptic problems in 2D;
the finite element formulation in 2D; a simple bilinear mesh for
the 2D problem.

Monday, 20 October:
Problem Sesssion, 2pm3pm, (Burkardt, Room 445)

Wednesday, 22 October:
Lecture: generating a mesh with Gmsh / Triangle / Mesh2D.
Storing a mesh in a file. The XML mesh file format used by FENICS.

Monday, 27 October:
Problem Sesssion, 2pm3pm, (Burkardt, Room 445)

Wednesday, 29 October:
Lecture (van Wyk):
The equations of potential flow.
Solving a potential flow problem using a region defined by
an XML mesh file.

Monday, 03 November:
Theory Sesssion, 2:45pm3:45pm (note time change!),
(van Wyk, Room 468),
Bilinear forms: Galerkin projection, best approximation.

Wednesday, 05 November:
Lecture: the steady heat equation; the steady Burgers equation

Monday, 10 November:
Theory Sesssion, 2:45pm4:15pm, (van Wyk, Room 468),
Riesz Representation, when the bilinear form is equivalent to a norm,
the weak derivative, the space H^m and its norm

Wednesday, 12 November:
Lecture: the time dependent heat equation

Monday, 17 November:
Theory Sesssion, 2:45pm3:45pm, (van Wyk, Room 468),
Sobolev spaces, the LaxMilgram theorem, Cea's Lemma.

Wednesday, 19 November:
Lecture (Burkardt/van Wyk):
the time dependent heat equation (last chance),
the steady Stokes flow problem for velocity and
pressure; defining a function space for (u,p); setting boundary
conditions; the variational form; special treatment of the
linear system

Monday, 24 November:
Theory Sesssion:

Wednesday, 26 November:
Lecture:

Monday, 01 December:
Theory Sesssion:

Wednesday, 03 December:
Lecture: NavierStokes problems
You can return to the
FEM 2014 web page.
Last revised on 19 November 2014.