Convergence of a residual based artificial viscosity finite element method

Murtazo Nazarov

doi:10.1016/j.camwa.2012.11.003

Convergence of a residual based artificial viscosity finite element method

Murtazo Nazarov

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.

Original language	English (US)
Pages (from-to)	616-626
Number of pages	11
Journal	Computers & Mathematics with Applications
Volume	65
Issue number	4
DOIs	https://doi.org/10.1016/j.camwa.2012.11.003
State	Published - Feb 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This material is based upon work supported by the Swedish Research Council (VR), and the Swedish Foundation for Strategic Research (SSF) and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.camwa.2012.11.003

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author = "Murtazo Nazarov",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: This material is based upon work supported by the Swedish Research Council (VR), and the Swedish Foundation for Strategic Research (SSF) and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AB - We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.

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JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

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ER -

Convergence of a residual based artificial viscosity finite element method

Abstract

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