Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity
HTML articles powered by AMS MathViewer

by Bernardo Cockburn, Weifeng Qiu and Manuel Solano PDF
Math. Comp. 83 (2014), 665-699 Request permission

Abstract:

We present the first a priori error analysis of a technique that allows us to numerically solve steady-state diffusion problems defined on curved domains $\Omega$ by using finite element methods defined in polyhedral subdomains $\mathsf {D}_h\subset \Omega$. For a wide variety of hybridizable discontinuous Galerkin and mixed methods, we prove that the order of convergence in the $L^2$-norm of the approximate flux and scalar unknowns is optimal as long as the distance between the boundary of the original domain $\Gamma$ and that of the computational domain $\Gamma _h$ is of order $h$. We also prove that the $L^2$-norm of a projection of the error of the scalar variable superconverges with a full additional order when the distance between $\Gamma$ and $\Gamma _h$ is of order $h^{5/4}$ but with only half an additional order when such a distance is of order $h$. Finally, we present numerical experiments confirming the theoretical results and showing that even when the distance between $\Gamma$ and $\Gamma _h$ is of order $h$, the above-mentioned projection of the error of the scalar variable can still superconverge with a full additional order.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65M60
  • Retrieve articles in all journals with MSC (2010): 65N30, 65M60
Additional Information
  • Bernardo Cockburn
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: cockburn@math.umn.edu
  • Weifeng Qiu
  • Affiliation: Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong
  • MR Author ID: 845089
  • Email: weifeqiu@cityu.edu.hk
  • Manuel Solano
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
  • Email: msolano@udel.edu
  • Received by editor(s): March 15, 2012
  • Received by editor(s) in revised form: July 6, 2012
  • Published electronically: July 18, 2013
  • Additional Notes: The first author was partially supported by the National Science Foundation (Grant DMS-1115331) and by the Minnesota Supercomputing Institute. The second author gratefully acknowledges the collaboration opportunities provided by the IMA during their 2011–12 program
    Corresponding author: Weifeng Qiu
  • © Copyright 2013 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 665-699
  • MSC (2010): Primary 65N30, 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02747-0
  • MathSciNet review: 3143688