Contributions to Books:
T. Wurzer, J. Melenk:
"Stability of the trace of the polynomial $L^2$-projection on triangles";
in: "ASC Report 36/2010",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
This bachelor thesis deals with the stability and approximation of the trace of the
polynomial L2-projection on triangles. We consider the L2-projection 2D
N : L2(T) !
PN(T) onto PN(T), where T is the reference triangle f(x; y) : 1 < x < 1;1 < y <
xg and show the following result
L2() CkukL2(T)kukH1(T); 8u 2 H1(T);
where we denote by one edge of @T.
At the end we will present a method to compute numerically the stability constant
C in the estimate above and show the computational results. We will also compute
two related stability constants, namely, the stability constant for the corresponding
N u)( 1)j2 CkukL2(1;1)kukH1(1;1); 8u 2 H1(1; 1);
N : L2(1; 1) ! PN(1; 1) is the L2-projection onto the space of polynomials
of degree N, and the stability constant CN in the two-dimensional bound
H1(T); 8u 2 H1(T):
Here, CN is seen to be O(N).
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.