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Superconvergence by $ M$-decompositions. Part I: General theory for HDG methods for diffusion


Authors: Bernardo Cockburn, Guosheng Fu and Francisco Javier Sayas
Journal: Math. Comp. 86 (2017), 1609-1641
MSC (2010): Primary 65M60, 65N30, 58J32, 65N15
DOI: https://doi.org/10.1090/mcom/3140
Published electronically: November 16, 2016
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Abstract: We introduce the concept of an $ M$-decomposition and show how to use it to systematically construct hybridizable discontinuous Galerkin and mixed methods for steady-state diffusion methods with superconvergence properties on unstructured meshes.


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Additional Information

Bernardo Cockburn
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: cockburn@math.umn.edu

Guosheng Fu
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: guosheng_fu@brown.edu

Francisco Javier Sayas
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: fjsayas@udel.edu

DOI: https://doi.org/10.1090/mcom/3140
Received by editor(s): December 29, 2014
Received by editor(s) in revised form: November 9, 2015, and December 26, 2015
Published electronically: November 16, 2016
Additional Notes: The first author was partially supported by the National Science Foundation (grant DMS-1115331)
The third author was partially supported by the National Science Foundation (grant DMS-1216356)
Article copyright: © Copyright 2016 American Mathematical Society