A nonlinear local projection stabilization for convection-diffusion-reaction equations

Gabriel Barrenechea; Volker John; Petr Knobloch

doi:10.1007/978-3-642-33134-3

A nonlinear local projection stabilization for convection-diffusion-reaction equations

Gabriel Barrenechea, Volker John, Petr Knobloch

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

Abstract

We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications 2011
Subtitle of host publication	Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011
Editors	A. Cangiani, R. L. Davidchack, E. H. Georgoulis, A. N. Gorban, J. Levesley, M. V. Tretyakov
Publisher	Springer-Verlag
Pages	237-245
Number of pages	9
ISBN (Electronic)	9783642331343
ISBN (Print)	9783642331336, 9783662511299
DOIs	https://doi.org/10.1007/978-3-642-33134-3
Publication status	Published - 10 Sept 2012
Event	ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications - University of Leicester, Leicester , United Kingdom Duration: 5 Sept 2011 → 9 Sept 2011

Conference

Conference	ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications
Abbreviated title	ENUMATH 2011
Country/Territory	United Kingdom
City	Leicester
Period	5/09/11 → 9/09/11

Keywords

numerical techniques
efficient computational techniques

Access to Document

10.1007/978-3-642-33134-3

Cite this

Barrenechea, G., John, V., & Knobloch, P. (2012). A nonlinear local projection stabilization for convection-diffusion-reaction equations. In A. Cangiani, R. L. Davidchack, E. H. Georgoulis, A. N. Gorban, J. Levesley, & M. V. Tretyakov (Eds.), Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 (pp. 237-245). Springer-Verlag. https://doi.org/10.1007/978-3-642-33134-3

Barrenechea, Gabriel ; John, Volker ; Knobloch, Petr. / A nonlinear local projection stabilization for convection-diffusion-reaction equations. Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. editor / A. Cangiani ; R. L. Davidchack ; E. H. Georgoulis ; A. N. Gorban ; J. Levesley ; M. V. Tretyakov. Springer-Verlag, 2012. pp. 237-245

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title = "A nonlinear local projection stabilization for convection-diffusion-reaction equations",

abstract = "We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.",

keywords = "numerical techniques, efficient computational techniques",

author = "Gabriel Barrenechea and Volker John and Petr Knobloch",

year = "2012",

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doi = "10.1007/978-3-642-33134-3",

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booktitle = "Numerical Mathematics and Advanced Applications 2011",

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note = "ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2011 ; Conference date: 05-09-2011 Through 09-09-2011",

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Barrenechea, G, John, V & Knobloch, P 2012, A nonlinear local projection stabilization for convection-diffusion-reaction equations. in A Cangiani, RL Davidchack, EH Georgoulis, AN Gorban, J Levesley & MV Tretyakov (eds), Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Springer-Verlag, pp. 237-245, ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester , United Kingdom, 5/09/11. https://doi.org/10.1007/978-3-642-33134-3

A nonlinear local projection stabilization for convection-diffusion-reaction equations. / Barrenechea, Gabriel; John, Volker; Knobloch, Petr.
Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. ed. / A. Cangiani; R. L. Davidchack; E. H. Georgoulis; A. N. Gorban; J. Levesley; M. V. Tretyakov. Springer-Verlag, 2012. p. 237-245.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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T1 - A nonlinear local projection stabilization for convection-diffusion-reaction equations

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AU - John, Volker

AU - Knobloch, Petr

PY - 2012/9/10

Y1 - 2012/9/10

N2 - We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.

AB - We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.

KW - numerical techniques

KW - efficient computational techniques

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DO - 10.1007/978-3-642-33134-3

M3 - Conference contribution book

SN - 9783642331336

SN - 9783662511299

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EP - 245

BT - Numerical Mathematics and Advanced Applications 2011

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A2 - Davidchack, R. L.

A2 - Georgoulis, E. H.

A2 - Gorban, A. N.

A2 - Levesley, J.

A2 - Tretyakov, M. V.

PB - Springer-Verlag

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Y2 - 5 September 2011 through 9 September 2011

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Barrenechea G, John V, Knobloch P. A nonlinear local projection stabilization for convection-diffusion-reaction equations. In Cangiani A, Davidchack RL, Georgoulis EH, Gorban AN, Levesley J, Tretyakov MV, editors, Numerical Mathematics and Advanced Applications 2011 : Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Springer-Verlag. 2012. p. 237-245 doi: 10.1007/978-3-642-33134-3

A nonlinear local projection stabilization for convection-diffusion-reaction equations

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