Multiwavelets and Jumps in DG Approximations

Mathea J. Vuik; Jennifer K. Ryan

doi:10.1007/978-3-319-19800-2_47

Multiwavelets and Jumps in DG Approximations

Mathea J. Vuik^*, Jennifer K. Ryan

^*Corresponding author for this work

Mathematical Physics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

6 Citations (Scopus)

Abstract

In general, solutions of nonlinear hyperbolic PDEs contain shocks or develop discontinuities. One option for improving the numerical treatment of the spurious oscillations that occur near these artifacts is through the application of a limiter. The cells where such treatment is necessary are referred to as troubled cells. In this article, we discuss the multiwavelet troubled-cell indicator that was introduced by Vuik and Ryan (J Comput Phys 270:138–160, 2014). We focus on the relation between the highest-level multiwavelet coefficients and jumps in (derivatives of) the DG approximation. Based on this information, we slightly modify the originalmultiwavelet troubled-cell indicator. Furthermore, we show onedimensional test cases using the modified multiwavelet troubled-cell indicator.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
Subtitle of host publication	Selected papers from the ICOSAHOM Conference
Editors	Robert M. Kirby, Martin Berzins, Jan S. Hesthaven
Place of Publication	Cham
Publisher	Springer
Pages	503-511
Number of pages	9
ISBN (Electronic)	978-3-319-19800-2
ISBN (Print)	978-3-319-19799-9
DOIs	https://doi.org/10.1007/978-3-319-19800-2_47
Publication status	Published - 2015
Event	ICOSAHOM 2014: International Conference on Spectral and High-Order Methods - Salt Lake City, UT, United States Duration: 23 Jun 2014 → 27 Jun 2014

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	106
ISSN (Print)	1439-7358

Conference

Conference	ICOSAHOM 2014
Country/Territory	United States
City	Salt Lake City, UT
Period	23/06/14 → 27/06/14

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10.1007/978-3-319-19800-2_47

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Vuik, M. J., & Ryan, J. K. (2015). Multiwavelets and Jumps in DG Approximations. In R. M. Kirby, M. Berzins, & J. S. Hesthaven (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM Conference (pp. 503-511). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer. https://doi.org/10.1007/978-3-319-19800-2_47

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title = "Multiwavelets and Jumps in DG Approximations",

abstract = "In general, solutions of nonlinear hyperbolic PDEs contain shocks or develop discontinuities. One option for improving the numerical treatment of the spurious oscillations that occur near these artifacts is through the application of a limiter. The cells where such treatment is necessary are referred to as troubled cells. In this article, we discuss the multiwavelet troubled-cell indicator that was introduced by Vuik and Ryan (J Comput Phys 270:138–160, 2014). We focus on the relation between the highest-level multiwavelet coefficients and jumps in (derivatives of) the DG approximation. Based on this information, we slightly modify the originalmultiwavelet troubled-cell indicator. Furthermore, we show onedimensional test cases using the modified multiwavelet troubled-cell indicator.",

author = "Vuik, {Mathea J.} and Ryan, {Jennifer K.}",

year = "2015",

doi = "10.1007/978-3-319-19800-2_47",

language = "English",

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editor = "Kirby, {Robert M.} and Martin Berzins and Hesthaven, {Jan S.}",

booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014",

note = "ICOSAHOM 2014 : International Conference on Spectral and High-Order Methods ; Conference date: 23-06-2014 Through 27-06-2014",

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Vuik, MJ & Ryan, JK 2015, Multiwavelets and Jumps in DG Approximations. in RM Kirby, M Berzins & JS Hesthaven (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM Conference. Lecture Notes in Computational Science and Engineering, vol. 106, Springer, Cham, pp. 503-511, ICOSAHOM 2014, Salt Lake City, UT, United States, 23/06/14. https://doi.org/10.1007/978-3-319-19800-2_47

Multiwavelets and Jumps in DG Approximations. / Vuik, Mathea J.; Ryan, Jennifer K.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014: Selected papers from the ICOSAHOM Conference. ed. / Robert M. Kirby; Martin Berzins; Jan S. Hesthaven. Cham: Springer, 2015. p. 503-511 (Lecture Notes in Computational Science and Engineering; Vol. 106).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AB - In general, solutions of nonlinear hyperbolic PDEs contain shocks or develop discontinuities. One option for improving the numerical treatment of the spurious oscillations that occur near these artifacts is through the application of a limiter. The cells where such treatment is necessary are referred to as troubled cells. In this article, we discuss the multiwavelet troubled-cell indicator that was introduced by Vuik and Ryan (J Comput Phys 270:138–160, 2014). We focus on the relation between the highest-level multiwavelet coefficients and jumps in (derivatives of) the DG approximation. Based on this information, we slightly modify the originalmultiwavelet troubled-cell indicator. Furthermore, we show onedimensional test cases using the modified multiwavelet troubled-cell indicator.

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Multiwavelets and Jumps in DG Approximations

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