Math/AMath 595: Finite Element Methods
(Winter 2001)
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Lectures: | MW 3:30-4:50, room 121 RAI
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Professor: | Anne Greenbaum, C-434 Padelford, 543-1175
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Office Hours: | MW after class - 6:00, or by appointment or drop in.
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e-mail: | greenbau@math.washington.edu
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Web Address: | http://www.math.washington.edu/~greenbau
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| Course materials: Click on ``Math/AMath 595". |
Text: Numerical solution of partial differential equations by the
finite element method, by Claes Johnson, Cambridge University Press, 1987.
(available at Professional Copy 'n' Print, 4200 University Way NE)
Reserve list: The following books are on reserve in the Mathematics
Research Library or are available in the Engineering Library.
- The Mathematical Theory of Finite Element Methods by Susanne C. Brenner
and L. Ridgway Scott (1994).
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The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet
(1978).
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An Analysis of the Finite Element Method by Gilbert Strang and George J.
Fix (1973).
The course will cover:
- Introduction to FEM for elliptic problems: Variational formulation of
a one-dimensional model problem; generating a finite element approximation
with piecewise linear functions; an error estimate for the model problem;
the Hilbert spaces L2 ( W), H1 ( W), and H01 ( W);
natural and essential boundary conditions.
- Abstract formulation of the finite element method for elliptic problems:
Generating a finite element approximation in two and more dimensions;
new problems encountered; regularity requirements; some finite element spaces;
error analysis for elliptic problems; the energy norm and the
L2 ( W)-norm.
- Some applications to elliptic problems.
- Direct and iterative methods for solving the systems of linear equations
arising from finite element approximations: Gaussian elimination; operation
counts; band matrices; the frontal method; nested dissection; the conjugate
gradient method; condition number of the stiffness matrix; preconditioning;
multigrid methods.
- FEM for parabolic and hyperbolic problems: semi-discretization in space;
adaptive methods in space and time.
There will be weekly homework assignments (with some programming) and
a course project. The project may involve using the finite element
method to solve a problem of your choice, reading and reporting on
a paper concerning aspects of the finite element method beyond those
covered in class, etc.
File translated from TEX by TTH, version 1.59.