DPG methods for a fourth-order div problem
Thomas Führer, Pablo Herrera and Norbert Heuer
Comput. Methods Appl. Math., 22 (3), 545–562, 2022.
We study a fourth-order div problem and its approximation by the discontinuous
Petrov–Galerkin method with optimal test functions.
We present two variants, based on first and second-order systems.
In both cases we prove well-posedness of the formulation and quasi-optimal convergence of
the approximation. Our analysis includes the fully-discrete schemes
with approximated test functions, for general dimension and polynomial degree in the
first-order case, and for two dimensions and lowest-order approximation in the second-order case.
Numerical results illustrate the performance for quasi-uniform and adaptively refined meshes.