Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations

In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come fro...

Full description

Saved in:
Bibliographic Details
Published in:Journal of scientific computing 2017-12, Vol.73 (2-3), p.1145-1163
Main Authors: Schütz, Jochen, Seal, David C., Jaust, Alexander
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Collocation methods
Computational Mathematics and Numerical Analysis
Convection-diffusion equation
Discretization
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Ordinary differential equations
Partial differential equations
Runge-Kutta method
Solvers
Theoretical
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-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43
cites cdi_FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43
container_end_page 1163
container_issue 2-3
container_start_page 1145
container_title Journal of scientific computing
container_volume 73
creator Schütz, Jochen
Seal, David C.
Jaust, Alexander
description In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax–Wendroff (Taylor) as well as Runge–Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.
doi_str_mv 10.1007/s10915-017-0485-9
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2918313573</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2918313573</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43</originalsourceid><addsrcrecordid>eNp1kM1KAzEURoMoWKsP4C7gejR3MpNMllK1FioK6jqkaaKp00mbzFT0EXxq007Blav83O98Fw5C50AugRB-FYEIKDMCPCNFVWbiAA2g5DTjTMAhGpAqffKCF8foJMYFIURUIh-gn8lyVTvtWvzQ1a2bm-A2qnUbg0e-rr1Od9_gZ19vTIjY-oCnrjEq4CcVWqdqfOOsNcE0u8ftutsBEX-69j3NovZp0nS-i3isahM-XGpbqT0adTCt--6ZU3RkVR3N2f4cote725fRfTZ9HE9G19NMU2BtlhNOS0rYvEiLZ5wTQYCpWW5yXnJNbWVhZjRVwFnJckUZZTATlS6BWZbbgg7RRd-7Cn7dmdjKhe9Ck1bKXEBFgSZvKQV9SgcfYzBWroJbqvAlgcitctkrl0m53CqXIjF5z8SUbd5M-Gv-H_oFSIGG3Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918313573</pqid></control><display><type>article</type><title>Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations</title><source>Springer Nature</source><creator>Schütz, Jochen ; Seal, David C. ; Jaust, Alexander</creator><creatorcontrib>Schütz, Jochen ; Seal, David C. ; Jaust, Alexander</creatorcontrib><description>In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax–Wendroff (Taylor) as well as Runge–Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-017-0485-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Accuracy ; Algorithms ; Collocation methods ; Computational Mathematics and Numerical Analysis ; Convection-diffusion equation ; Discretization ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Ordinary differential equations ; Partial differential equations ; Runge-Kutta method ; Solvers ; Theoretical</subject><ispartof>Journal of scientific computing, 2017-12, Vol.73 (2-3), p.1145-1163</ispartof><rights>Springer Science+Business Media, LLC (outside the USA) 2017</rights><rights>Springer Science+Business Media, LLC (outside the USA) 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43</citedby><cites>FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Schütz, Jochen</creatorcontrib><creatorcontrib>Seal, David C.</creatorcontrib><creatorcontrib>Jaust, Alexander</creatorcontrib><title>Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax–Wendroff (Taylor) as well as Runge–Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.</description><subject>Accuracy</subject><subject>Algorithms</subject><subject>Collocation methods</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convection-diffusion equation</subject><subject>Discretization</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Ordinary differential equations</subject><subject>Partial differential equations</subject><subject>Runge-Kutta method</subject><subject>Solvers</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KAzEURoMoWKsP4C7gejR3MpNMllK1FioK6jqkaaKp00mbzFT0EXxq007Blav83O98Fw5C50AugRB-FYEIKDMCPCNFVWbiAA2g5DTjTMAhGpAqffKCF8foJMYFIURUIh-gn8lyVTvtWvzQ1a2bm-A2qnUbg0e-rr1Od9_gZ19vTIjY-oCnrjEq4CcVWqdqfOOsNcE0u8ftutsBEX-69j3NovZp0nS-i3isahM-XGpbqT0adTCt--6ZU3RkVR3N2f4cote725fRfTZ9HE9G19NMU2BtlhNOS0rYvEiLZ5wTQYCpWW5yXnJNbWVhZjRVwFnJckUZZTATlS6BWZbbgg7RRd-7Cn7dmdjKhe9Ck1bKXEBFgSZvKQV9SgcfYzBWroJbqvAlgcitctkrl0m53CqXIjF5z8SUbd5M-Gv-H_oFSIGG3Q</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>Schütz, Jochen</creator><creator>Seal, David C.</creator><creator>Jaust, Alexander</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20171201</creationdate><title>Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations</title><author>Schütz, Jochen ; Seal, David C. ; Jaust, Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Accuracy</topic><topic>Algorithms</topic><topic>Collocation methods</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Convection-diffusion equation</topic><topic>Discretization</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Methods</topic><topic>Ordinary differential equations</topic><topic>Partial differential equations</topic><topic>Runge-Kutta method</topic><topic>Solvers</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schütz, Jochen</creatorcontrib><creatorcontrib>Seal, David C.</creatorcontrib><creatorcontrib>Jaust, Alexander</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schütz, Jochen</au><au>Seal, David C.</au><au>Jaust, Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2017-12-01</date><risdate>2017</risdate><volume>73</volume><issue>2-3</issue><spage>1145</spage><epage>1163</epage><pages>1145-1163</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>In this work, we construct novel discretizations for the unsteady convection–diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unkowns for the solver. These type of temporal discretizations come from an umbrella class of methods that include Lax–Wendroff (Taylor) as well as Runge–Kutta methods as special cases. We include two-point collocation methods with multiple time derivatives as well as a sixth-order fully implicit collocation method that only requires a total of three stages. Numerical results for a number of sample linear problems indicate the expected order of accuracy and indicate we can take arbitrarily large time steps.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-017-0485-9</doi><tpages>19</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0885-7474
ispartof Journal of scientific computing, 2017-12, Vol.73 (2-3), p.1145-1163
issn 0885-7474
1573-7691
language eng
recordid cdi_proquest_journals_2918313573
source Springer Nature
subjects Accuracy
Algorithms
Collocation methods
Computational Mathematics and Numerical Analysis
Convection-diffusion equation
Discretization
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Ordinary differential equations
Partial differential equations
Runge-Kutta method
Solvers
Theoretical
title Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-30T21%3A42%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Implicit%20Multiderivative%20Collocation%20Solvers%20for%20Linear%20Partial%20Differential%20Equations%20with%20Discontinuous%20Galerkin%20Spatial%20Discretizations&rft.jtitle=Journal%20of%20scientific%20computing&rft.au=Sch%C3%BCtz,%20Jochen&rft.date=2017-12-01&rft.volume=73&rft.issue=2-3&rft.spage=1145&rft.epage=1163&rft.pages=1145-1163&rft.issn=0885-7474&rft.eissn=1573-7691&rft_id=info:doi/10.1007/s10915-017-0485-9&rft_dat=%3Cproquest_cross%3E2918313573%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c316t-20735306d4ffeb7709016ab2e2757c3f8f1bec3a176562a36361b98c516f62f43%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2918313573&rft_id=info:pmid/&rfr_iscdi=true