MONDAY, NOVEMBER 6, 2006

DE/Applied and Computational Math Seminar

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 309A
SPEAKER: Professor Xiaobing Feng
TITLE: Vanishing Moment Method and Notion of Moment Solution for 2rd Order Fully Nonlinear PDEs

WEDNESDAY, NOVEMBER 8, 2006

GRADUATE STUDENT TEACHING SEMINAR
Website: http://www.math.utk.edu/~eaton/Math598.htm (for handouts and updated schedule of events)

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 314
TITLE: Technology in the Classroom: Using the Smart Classroom and Other Classroom Technology
We meet in a “smart” room. Do you know what a “smart” room is? Do you know about its potential? How can we take advantage of today’s technology to ease our responsibilities and make our teaching more interactive and effective? We will hear how Bob Guest uses Excel, how Amy Szczepanski uses her iPod, and how Carrie Eaton used online technology in class and got $500 for a new laptop.

ANALYSIS SEMINAR

TIME: 3:35 p.m. - 4:25 p.m.
ROOM: Ayres Hall 320
SPEAKER: Gerald Orick
TITLE: Aleksandrov's Characterization of Cauchy Transforms 2


FRIDAY, NOVEMBER 10, 2006

COLLOQUIUM

TIME: 3:35 – 4:35 p.m.
ROOM: 214 Ayres Hall
SPEAKER: Professor Michael Plum, University of Karlsruhe
Institute for Analysis
TITLE: Enclosure methods and computer-assisted proofs for elliptic boundary value problems
ABSTRACT: The lecture will be concerned with numerical enclosure methods for nonlinear elliptic boundary value problems. Here, analytical and numerical methods are combined to prove rigorously the existence of a solution in some "close" neighborhood of an approximate solution computed by numerical means. Thus, besides the existence proof, verified bounds for the error (i.e. the difference between exact and approximate solution) are provided.

For the first step, consisting of the computation of an approximate solution w in some appropriate Sobolev space, no error control is needed, so a wide range of well-established numerical methods (including Multigrid schemes) is at hand here. Using w, the given problem is rewritten as a fixed-point equation for the error, and the goal is to apply a fixed-point theorem providing the desired error bound.

The conditions required by the chosen fixed-point theorem (e.g., compactness or contractivity, inclusion properties for a suitable subset etc.) are now verified by a combination of analytical arguments (e.g. explicit Sobolev embeddings, variational characterizations etc.) and verified computations of certain auxiliary terms, in particular of eigenvalue bounds for the linearization of the given problem at w.

The method is illustrated by several examples (on bounded as well as on unbounded domains), where in particular it gives existence proofs in cases where no purely analytical proof is known.


REFRESHMENTS WILL BE SERVED IN AYRES HALL ROOM 119 AT 3:00 P.M.