Superconvergence by -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
MathSciNet review:
3626530
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Abstract | References | Similar Articles | Additional Information
Abstract: We introduce the concept of an -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