Computing the -Numerical Range of Differential Operators

Figure 2

On the left-hand side, the variational method approximation to the Stokes operator. The approximation is given by a real symmetric matrix with some eigenvalues with The -numerical range of for is the line segment ; the red dots are . On the right-hand side, the q-numerical range of for is the union of closed circular disk center at with radius where The small red circles inside the circular disk are scaled by .