2026-09-20T04:24:38Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1056082022-01-13T07:53:53Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
David L. Darmofal.
Carson, Hugh Alexander
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2016-12-05T19:54:46Z
2016-12-05T19:54:46Z
2016
2016
http://hdl.handle.net/1721.1/105608
962485917
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 103-105).
In this thesis, a priori convergence estimates are developed for outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved convergence rates relative to the common approach utilizing statically condensed, p-dependent lifting operators. The HDG output error estimates are new and include the impact of stabilization. Comparisons to numerical results demonstrate (1) the sharpness of the estimates and (2) that the HDG estimates are approximately an order of magnitude more accurate than CG and DG.
by Hugh Alexander Carson.
S.M.
105 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Aeronautics and Astronautics.
A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations
Thesis
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<Abstract>In this thesis, a priori convergence estimates are developed for outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved convergence rates relative to the common approach utilizing statically condensed, p-dependent lifting operators. The HDG output error estimates are new and include the impact of stabilization. Comparisons to numerical results demonstrate (1) the sharpness of the estimates and (2) that the HDG estimates are approximately an order of magnitude more accurate than CG and DG.</Abstract>
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