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Devising superconvergent HDG methods...

Shi, Ke.

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Devising superconvergent HDG methods for partial differential equations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Devising superconvergent HDG methods for partial differential equations./
Author:	Shi, Ke.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2012,
Description:	174 p.
Notes:	Source: Dissertations Abstracts International, Volume: 74-04, Section: B.
Contained By:	Dissertations Abstracts International74-04B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3540939
ISBN:	9781267667595

Devising superconvergent HDG methods for partial differential equations.
Shi, Ke.

Devising superconvergent HDG methods for partial differential equations. - Ann Arbor : ProQuest Dissertations & Theses, 2012 - 174 p.

Source: Dissertations Abstracts International, Volume: 74-04, Section: B.

Thesis (Ph.D.)--University of Minnesota, 2012.

The DG methods are ideally suited for numerically solving hyperbolic problems. However this is not the case for diffusion problems, even though they are ideally suited for hp-adaptivity. Indeed, when compared with the classical continuous Galerkin methods on the same mesh, they have many more global degrees of freedom and they are not easy to implement. When compared with the mixed methods, they do not provide optimally convergent approximations to the flux and do not display superconvergence properties of the scalar variable. As a response to these disadvantages, the HDG methods were introduced. Therein, it was shown that HDG methods can be implemented as efficiently as the mixed methods. Later it was proven that the HDG methods do share with mixed methods their superior convergence properties while retaining the advantages typical of the DG methods. Inspired by these results, in this Thesis we are trying to explore HDG methods in a wider circumstance.

ISBN: 9781267667595Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Discontinuous galerkin

Devising superconvergent HDG methods for partial differential equations.
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245 1 0 $a Devising superconvergent HDG methods for partial differential equations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2012
300 $a 174 p.
500 $a Source: Dissertations Abstracts International, Volume: 74-04, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Cockburn, Bernardo.
502 $a Thesis (Ph.D.)--University of Minnesota, 2012.
520 $a The DG methods are ideally suited for numerically solving hyperbolic problems. However this is not the case for diffusion problems, even though they are ideally suited for hp-adaptivity. Indeed, when compared with the classical continuous Galerkin methods on the same mesh, they have many more global degrees of freedom and they are not easy to implement. When compared with the mixed methods, they do not provide optimally convergent approximations to the flux and do not display superconvergence properties of the scalar variable. As a response to these disadvantages, the HDG methods were introduced. Therein, it was shown that HDG methods can be implemented as efficiently as the mixed methods. Later it was proven that the HDG methods do share with mixed methods their superior convergence properties while retaining the advantages typical of the DG methods. Inspired by these results, in this Thesis we are trying to explore HDG methods in a wider circumstance.
590 $a School code: 0130.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
653 $a Discontinuous galerkin
653 $a Finite element
653 $a Fluid mechanics
653 $a Hybridizable
653 $a Numerical analysis
653 $a Partial differential equations
653 $a Superconvergent HDG
690 $a 0364
690 $a 0405
710 2 $a University of Minnesota. $b Mathematics. $3 1675975
773 0 $t Dissertations Abstracts International $g 74-04B.
790 $a 0130
791 $a Ph.D.
792 $a 2012
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3540939