A DPG method for the quad-curl problem
Thomas Führer, Pablo Herrera and Norbert Heuer
Comput. Math. Appl. 149, 221–238, 2023.
We derive an ultraweak variational formulation of the quad-curl problem
in two and three dimensions. We present a discontinuous Petrov–Galerkin
(DPG) method for its approximation and prove its quasi-optimal convergence.
We illustrate how this method can be applied to the Stokes problem in
two dimensions, after an application of the curl operator to eliminate the
pressure variable. In this way, DPG techniques known from Kirchhoff–Love
plates can be used. We present an a priori error estimate that improves a
previous approximation result for effective shear forces by using a less
restrictive regularity assumption.
Numerical experiments illustrate our findings.