Convergence rates of the DPG method with reduced test space degree. (English) Zbl 1364.65239
Summary: 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.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
least-squares; discontinuous Petrov-Galerkin; DPG method; strang lemma; Aubin-Nitsche; duality argumentReferences:
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