This work was partially supported by the NSF under grant DMS-1318916 and by the AFOSR under grant FA9550-12-1-0484.
Stochastic convergence, Discontinuous functions, Galerkin methods, Laplace's equation, Numerical analysis
This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (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
Bouma, Timaeus; Gopalakrishnan, Jay; and Harb, Ammar, "Convergence Rates of the DPG Method with Reduced Test Space Degree" (2014). Mathematics and Statistics Faculty Publications and Presentations. 86.