High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation

We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipati...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2022-06, Vol.407 (C), p.114015, Article 114015
Main Authors: Liu, Hailiang, Yin, Peimeng
Format: Article
Language:English
Subjects:
DG methods
Energy stability
EQ approach
Gradient flows
RK method
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043
cites cdi_FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043
container_end_page
container_issue C
container_start_page 114015
container_title Journal of computational and applied mathematics
container_volume 407
creator Liu, Hailiang
Yin, Peimeng
description We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm.
doi_str_mv 10.1016/j.cam.2021.114015
format article
fullrecord <record><control><sourceid>elsevier_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_1840087</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042721005987</els_id><sourcerecordid>S0377042721005987</sourcerecordid><originalsourceid>FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEqXwAews9gl2nMaOWCEeLaISEg-JneXY48ZVmoDtgrrjH_hDvoREYc1qFnPv0cxB6JSSlBJanK9TrTZpRjKaUpoTOttDEyp4mVDOxT6aEMZ5QvKMH6KjENaEkKKk-QS9Ltyqxp034PG21V1rXHRdq5pmh6EFv9rhEFXVAH68v57joGvYQMC28zjWgJ8-nY0_X9-Lroa26uMY3rdqIByjA6uaACd_c4pebm-erxbJ8mF-d3W5TDQreExMxazJRAbCMrCWK2q0qbiYiSoXdFYqm1X9ivHC8JxTVhSKcMJKloEqKpKzKTobuV2ITgbtIui6_6MFHSUVOSGC9yE6hrTvQvBg5Zt3G-V3khI5-JNr2fuTgz85-us7F2MH-us_HPgBDq0G4_zANp37p_0LOY95Rg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation</title><source>ScienceDirect Freedom Collection 2022-2024</source><creator>Liu, Hailiang ; Yin, Peimeng</creator><creatorcontrib>Liu, Hailiang ; Yin, Peimeng</creatorcontrib><description>We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2021.114015</identifier><language>eng</language><publisher>Belgium: Elsevier B.V</publisher><subject>DG methods ; Energy stability ; EQ approach ; Gradient flows ; RK method</subject><ispartof>Journal of computational and applied mathematics, 2022-06, Vol.407 (C), p.114015, Article 114015</ispartof><rights>2021 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043</citedby><cites>FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043</cites><orcidid>0000-0002-9188-8011 ; 0000000291888011</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/1840087$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Hailiang</creatorcontrib><creatorcontrib>Yin, Peimeng</creatorcontrib><title>High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation</title><title>Journal of computational and applied mathematics</title><description>We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm.</description><subject>DG methods</subject><subject>Energy stability</subject><subject>EQ approach</subject><subject>Gradient flows</subject><subject>RK method</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwAews9gl2nMaOWCEeLaISEg-JneXY48ZVmoDtgrrjH_hDvoREYc1qFnPv0cxB6JSSlBJanK9TrTZpRjKaUpoTOttDEyp4mVDOxT6aEMZ5QvKMH6KjENaEkKKk-QS9Ltyqxp034PG21V1rXHRdq5pmh6EFv9rhEFXVAH68v57joGvYQMC28zjWgJ8-nY0_X9-Lroa26uMY3rdqIByjA6uaACd_c4pebm-erxbJ8mF-d3W5TDQreExMxazJRAbCMrCWK2q0qbiYiSoXdFYqm1X9ivHC8JxTVhSKcMJKloEqKpKzKTobuV2ITgbtIui6_6MFHSUVOSGC9yE6hrTvQvBg5Zt3G-V3khI5-JNr2fuTgz85-us7F2MH-us_HPgBDq0G4_zANp37p_0LOY95Rg</recordid><startdate>202206</startdate><enddate>202206</enddate><creator>Liu, Hailiang</creator><creator>Yin, Peimeng</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0002-9188-8011</orcidid><orcidid>https://orcid.org/0000000291888011</orcidid></search><sort><creationdate>202206</creationdate><title>High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation</title><author>Liu, Hailiang ; Yin, Peimeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>DG methods</topic><topic>Energy stability</topic><topic>EQ approach</topic><topic>Gradient flows</topic><topic>RK method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Hailiang</creatorcontrib><creatorcontrib>Yin, Peimeng</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Hailiang</au><au>Yin, Peimeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2022-06</date><risdate>2022</risdate><volume>407</volume><issue>C</issue><spage>114015</spage><pages>114015-</pages><artnum>114015</artnum><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>We propose unconditionally energy stable Runge–Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows including the Swift–Hohenberg equation. Our algorithm is geared toward arbitrarily high order approximations in both space and time, while energy dissipation remains preserved for arbitrary time steps and spatial meshes. The method integrates a penalty free DG method for spatial discretization with a multi-stage algebraically stable RK method for temporal discretization by the energy quadratiztion (EQ) strategy. The resulting fully discrete DG method is proven to be unconditionally energy stable. By numerical tests on several benchmark problems we demonstrate the high order accuracy, energy stability, and simplicity of the proposed algorithm.</abstract><cop>Belgium</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2021.114015</doi><orcidid>https://orcid.org/0000-0002-9188-8011</orcidid><orcidid>https://orcid.org/0000000291888011</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0377-0427
ispartof Journal of computational and applied mathematics, 2022-06, Vol.407 (C), p.114015, Article 114015
issn 0377-0427
1879-1778
language eng
recordid cdi_osti_scitechconnect_1840087
source ScienceDirect Freedom Collection 2022-2024
subjects DG methods
Energy stability
EQ approach
Gradient flows
RK method
title High order unconditionally energy stable RKDG schemes for the Swift–Hohenberg equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-22T06%3A38%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=High%20order%20unconditionally%20energy%20stable%20RKDG%20schemes%20for%20the%20Swift%E2%80%93Hohenberg%20equation&rft.jtitle=Journal%20of%20computational%20and%20applied%20mathematics&rft.au=Liu,%20Hailiang&rft.date=2022-06&rft.volume=407&rft.issue=C&rft.spage=114015&rft.pages=114015-&rft.artnum=114015&rft.issn=0377-0427&rft.eissn=1879-1778&rft_id=info:doi/10.1016/j.cam.2021.114015&rft_dat=%3Celsevier_osti_%3ES0377042721005987%3C/elsevier_osti_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c367t-db3fd282e8f3eff7a1dcdb7858b48159af2b8f3376d7471366a0703932ea6b043%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true