Convergence rates of the DPG method with reduced test space degree ?
This paper presents a duality theorem of the AubinNitsche type for discontinuous PetrovGalerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree.
dpg method aubinnitsche discontinuous petrovgalerkin least-squares strang lemma duality argument