Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

Antti H. Niemi; Nathaniel O. Collier; Victor M. Calo

doi:10.1016/j.procs.2011.04.202

Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

Antti H. Niemi, Nathaniel O. Collier, Victor M. Calo

Research output: Contribution to journal › Conference article › peer-review

12 Scopus citations

Abstract

We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation.

Original language	English
Pages (from-to)	1862-1869
Number of pages	8
Journal	Procedia Computer Science
Volume	4
DOIs	https://doi.org/10.1016/j.procs.2011.04.202
State	Published - 2011
Externally published	Yes
Event	11th International Conference on Computational Science, ICCS 2011 - Singapore, Singapore Duration: Jun 1 2011 → Jun 3 2011

Keywords

Convection-diffusion
Discontinuous Petrov-Galerkin
Finite element method

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10.1016/j.procs.2011.04.202

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title = "Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems",

abstract = "We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation.",

keywords = "Convection-diffusion, Discontinuous Petrov-Galerkin, Finite element method",

author = "Niemi, {Antti H.} and Collier, {Nathaniel O.} and Calo, {Victor M.}",

year = "2011",

doi = "10.1016/j.procs.2011.04.202",

language = "English",

volume = "4",

pages = "1862--1869",

journal = "Procedia Computer Science",

issn = "1877-0509",

publisher = "Elsevier",

note = "11th International Conference on Computational Science, ICCS 2011 ; Conference date: 01-06-2011 Through 03-06-2011",

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TY - JOUR

T1 - Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

AU - Niemi, Antti H.

AU - Collier, Nathaniel O.

AU - Calo, Victor M.

PY - 2011

Y1 - 2011

N2 - We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation.

AB - We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation.

KW - Convection-diffusion

KW - Discontinuous Petrov-Galerkin

KW - Finite element method

UR - http://www.scopus.com/inward/record.url?scp=79958289254&partnerID=8YFLogxK

U2 - 10.1016/j.procs.2011.04.202

DO - 10.1016/j.procs.2011.04.202

M3 - Conference article

AN - SCOPUS:79958289254

SN - 1877-0509

VL - 4

SP - 1862

EP - 1869

JO - Procedia Computer Science

JF - Procedia Computer Science

T2 - 11th International Conference on Computational Science, ICCS 2011

Y2 - 1 June 2011 through 3 June 2011

ER -

Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

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Keywords

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