Analysis and Operator Theory Seminar - Lyonell Boulton

September 4, 2019
Tuesday, September 17, 2019 - 2:00pm to 2:55pm
Cockins Hall 240
Analysis and Operator Theory Seminar

Title: Numerical approximation of Poincare - Friedrichs constants

Speaker: Lyonell Boulton, Heriot-Watt University

Abstract: The amplitude of a regular function which vanishes on the boundary of a compact region is controlled (integral square) by a constant times the gradient. The smallest possible value of the constant, allowing this to hold true for all functions in the suitable Sobolev space, is non-zero and it is often called the Poincare - Friedrichs constant. A similar statement is still valid, if we replace the gradient by the curl operator on fields with zero divergence subject to suitable boundary conditions.

Unfortunately, we cannot estimate numerically guaranteed upper bounds for Poincaré- Friedrichs constants by means of a direct application of the classical Galerkin method. The latter might lead, for example, to variational collapse in the case of the curl operator. In this talk I will present two methods for overcoming this difficulty for I) the gradient on regions with very rough boundary and II) the curl on regions with re-entrant corners.

S M T W T F S
1
 
2
 
3
 
4
 
5
 
6
 
7
 
8
 
9
 
10
 
11
 
12
 
13
 
14
 
15
 
16
 
17
 
18
 
19
 
20
 
21
 
22
 
23
 
24
 
25
 
26
 
27
 
28
 
29
 
30