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Automatically stable discontinuous Petrov–Galerkin methods for stationary transport problems: Quasi-optimal test space norm
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2013 (English)In: Computers & Mathematics with Applications, ISSN 0898-1221Article in journal (Refereed) Published
Abstract [en]

We investigate the application of the discontinuous Petrov–Galerkin (DPG) finite element framework to stationary convection–diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view.

Place, publisher, year, edition, pages
National Category
Subatomic Physics
Research subject
Theoretical Physics
URN: urn:nbn:se:uu:diva-287791DOI: 10.1016/j.camwa.2013.07.016OAI: oai:DiVA.org:uu-287791DiVA: diva2:923459
Available from: 2016-04-26 Created: 2016-04-26 Last updated: 2016-04-26

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Publisher's full texthttp://www.sciencedirect.com/science/article/pii/S0898122113004446?np=y

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Niemi, Antti
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