2 research outputs found
A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs
We investigated an hybridizable discontinuous Galerkin (HDG) method for a
convection diffusion Dirichlet boundary control problem in our earlier work
[SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence
rate for the control under some assumptions on the desired state and the
domain. In this work, we obtain the same convergence rate for the control using
a class of embedded DG methods proposed by Nguyen, Peraire and Cockburn [J.
Comput. Phys. vol. 302 (2015), pp. 674-692] for simulating fluid flows. Since
the global system for embedded DG methods uses continuous elements, the number
of degrees of freedom for the embedded DG methods are smaller than the HDG
method, which uses discontinuous elements for the global system. Moreover, we
introduce a new simpler numerical analysis technique to handle low regularity
solutions of the boundary control problem. We present some numerical
experiments to confirm our theoretical results