DPG method with optimal test functions for a transmission problem
Norbert Heuer and Michael Karkulik
Comput. Math. Appl. 70 (5), 1504-1518, 2015.
We propose and analyze a numerical method to solve an elliptic transmission
problem in full space. The method consists of a variational formulation
involving standard boundary integral operators on the coupling interface
and an ultra-weak formulation in the interior.
To guarantee the discrete inf-sup condition, the system is discretized
by the DPG method with optimal test functions.
We prove that principal unknowns are approximated quasi-optimally.
Numerical experiments for problems with smooth and singular solutions
confirm optimal convergence orders.