A non-overlapping domain decomposition method for parabolic initial-boundary value problems
A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerki...
Gespeichert in:
| Veröffentlicht in: | Applied numerical mathematics Jg. 28; H. 2; S. 359 - 369 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
01.10.1998
Elsevier |
| Schlagworte: | |
| ISSN: | 0168-9274, 1873-5460 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerkin method in space. A convergence proof is available in appropriate Sobolev norms for the continuous elliptic problems arising in each time step. The numerical convergence rate is independent of the mesh size. Finally we extend the approach to more complex problems. |
|---|---|
| AbstractList | A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerkin method in space. A convergence proof is available in appropriate Sobolev norms for the continuous elliptic problems arising in each time step. The numerical convergence rate is independent of the mesh size. Finally we extend the approach to more complex problems. |
| Author | Lube, G. Müller, H. Otto, F.C. |
| Author_xml | – sequence: 1 givenname: G. surname: Lube fullname: Lube, G. email: lube@math.uni-goettingen.de organization: Fakultät für Mathematik, Universität Göttingen, D-37083 Göttingen, Germany – sequence: 2 givenname: F.C. surname: Otto fullname: Otto, F.C. organization: Fakultät für Mathematik, Universität Göttingen, D-37083 Göttingen, Germany – sequence: 3 givenname: H. surname: Müller fullname: Müller, H. organization: Fakultät für Maschinenwesen, Technische Universität Dresden, D-01062 Dresden, Germany |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1603869$$DView record in Pascal Francis |
| BookMark | eNqFkE1LxDAURYOM4MzoTxCycKGLatK0aYILGQa_YMCFunIR0nxopE1K0hnw39vOiIKb2by3eOdeHmcGJj54A8ApRpcYYXr1PAyW8bwqzjm7QAiVJMMHYIpZRbKyoGgCpr_IEZil9DlCZYGm4G0Bh7YsbExsZNc5_w51aKXzUBsV2i4k17vgYWv6j6ChDRF2Mso6NE5B54ejbLI6rL2W8QtuZLM2sIuhbkybjsGhlU0yJz97Dl7vbl-WD9nq6f5xuVhlihDaZ7kulNKktNxqYnNCsKbDp1YjRYuqwrgoa84IzrXCOa-M5kpRxnJOaYllXpM5ONv1djIp2dgovXJJdNG1w1MCU0QY5QNW7jAVQ0rR2D8CiVGk2IoUoyXBmdiKFHjIXf_LKdfL0UofpWv2pm92aTMY2DgTRVLOeGW0i0b1Qge3p-Eb8qKP-A |
| CODEN | ANMAEL |
| CitedBy_id | crossref_primary_10_1016_S0017_9310_00_00299_4 crossref_primary_10_1016_j_compfluid_2012_04_018 crossref_primary_10_1016_j_camwa_2023_10_011 crossref_primary_10_1016_S0168_9274_01_00177_5 crossref_primary_10_1016_j_automatica_2021_110109 crossref_primary_10_1080_10407790_2023_2207734 crossref_primary_10_1016_j_amc_2010_09_059 |
| Cites_doi | 10.1016/0168-9274(95)00024-O 10.1007/BF02510246 10.1142/S021820259500005X 10.1016/0045-7825(91)90145-V 10.1142/S0218202598000500 |
| ContentType | Journal Article Conference Proceeding |
| Copyright | 1998 1999 INIST-CNRS |
| Copyright_xml | – notice: 1998 – notice: 1999 INIST-CNRS |
| DBID | AAYXX CITATION IQODW |
| DOI | 10.1016/S0168-9274(98)00053-1 |
| DatabaseName | CrossRef Pascal-Francis |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1873-5460 |
| EndPage | 369 |
| ExternalDocumentID | 1603869 10_1016_S0168_9274_98_00053_1 S0168927498000531 |
| GrantInformation_xml | – fundername: International Association for Mathematics and Computers in Simulation |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD AEBSH AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HMJ HVGLF HZ~ IHE J1W KOM M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SSW SSZ T5K TN5 VH1 VOH WH7 WUQ XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD BNPGV IQODW SSH |
| ID | FETCH-LOGICAL-c336t-2d4ccd35f9fd3f2331d6927fd0c64771145b98312dc1297ed9cc688296651a2b3 |
| ISICitedReferencesCount | 12 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000076563000018&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-9274 |
| IngestDate | Wed Apr 02 07:25:15 EDT 2025 Sat Nov 29 02:29:35 EST 2025 Tue Nov 18 20:55:31 EST 2025 Fri Feb 23 02:29:21 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Advection-reaction-diffusion Non-overlapping domain decomposition method Grid pattern Initial value problem Advection diffusion equation Numerical method Partial differential equation Discretization method Galerkin-Petrov method Parabolic equation Elliptic equation Boundary value problem Convergence rate Domain decomposition Numerical convergence |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MeetingName | NUMDIFF-8: Conference on the Numerical Treatment of Differential Equations |
| MergedId | FETCHMERGED-LOGICAL-c336t-2d4ccd35f9fd3f2331d6927fd0c64771145b98312dc1297ed9cc688296651a2b3 |
| PageCount | 11 |
| ParticipantIDs | pascalfrancis_primary_1603869 crossref_primary_10_1016_S0168_9274_98_00053_1 crossref_citationtrail_10_1016_S0168_9274_98_00053_1 elsevier_sciencedirect_doi_10_1016_S0168_9274_98_00053_1 |
| PublicationCentury | 1900 |
| PublicationDate | 1998-10-01 |
| PublicationDateYYYYMMDD | 1998-10-01 |
| PublicationDate_xml | – month: 10 year: 1998 text: 1998-10-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Applied numerical mathematics |
| PublicationYear | 1998 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Auge, Kapurkin, Lube, Otto (BIB1) 1996 Lube, Weiss (BIB8) 1995; 17 Auge, Lube, Otto (BIB2) 1997 Kusnetzov (BIB5) 1990 Lube, Otto (BIB7) 1997 Gastaldi, Gastaldi, Quarteroni (BIB4) 1996; 4 Otto, Lube (BIB10) 1998 Thomee (BIB13) 1997 Douglas, Huang (BIB3) 1997; 37 Le Tallec (BIB6) 1994; 1 Rannacher, Zhou (BIB11) 1994; 2 Nataf, Rogier (BIB9) 1995; 5 Shakib, Hughes (BIB12) 1991; 87 Douglas (10.1016/S0168-9274(98)00053-1_BIB3) 1997; 37 Kusnetzov (10.1016/S0168-9274(98)00053-1_BIB5) 1990 Rannacher (10.1016/S0168-9274(98)00053-1_BIB11) 1994; 2 Gastaldi (10.1016/S0168-9274(98)00053-1_BIB4) 1996; 4 Le Tallec (10.1016/S0168-9274(98)00053-1_BIB6) 1994; 1 Shakib (10.1016/S0168-9274(98)00053-1_BIB12) 1991; 87 Auge (10.1016/S0168-9274(98)00053-1_BIB1) 1996 Otto (10.1016/S0168-9274(98)00053-1_BIB10) 1998 Thomee (10.1016/S0168-9274(98)00053-1_BIB13) 1997 Lube (10.1016/S0168-9274(98)00053-1_BIB7) 1997 Nataf (10.1016/S0168-9274(98)00053-1_BIB9) 1995; 5 Auge (10.1016/S0168-9274(98)00053-1_BIB2) 1997 Lube (10.1016/S0168-9274(98)00053-1_BIB8) 1995; 17 |
| References_xml | – volume: 4 start-page: 165 year: 1996 end-page: 206 ident: BIB4 article-title: Adaptive domain decomposition methods for advection dominated equations publication-title: East-West J. Numer. Math. – volume: 17 start-page: 431 year: 1995 end-page: 459 ident: BIB8 article-title: Stabilized finite element methods for singularly perturbed parabolic problems publication-title: Appl. Numer. Math. – year: 1998 ident: BIB10 article-title: A non-overlapping domain decomposition method for the Oseen equations publication-title: Math. Models Methods Appl. Sci. – start-page: 71 year: 1997 end-page: 80 ident: BIB7 article-title: A non-overlapping domain decomposition method for incompressible flow problems publication-title: Proc. 3rd Summer Conf. – volume: 87 start-page: 35 year: 1991 end-page: 58 ident: BIB12 article-title: A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms publication-title: Comput. Methods Appl. Mech. Engrg. – start-page: 211 year: 1990 end-page: 227 ident: BIB5 article-title: Domain decomposition methods for unsteady convection-diffusion problems publication-title: Proc. 9th Int. Conf. on Comput. Methods Appl. Sci. Engrg. – volume: 37 start-page: 678 year: 1997 end-page: 686 ident: BIB3 article-title: An accelerated domain decomposition procedure based on Robin transmission conditions publication-title: BIT – year: 1996 ident: BIB1 article-title: A note on domain decomposition of singularly perturbed elliptic problems publication-title: Proc. of DDM9 Conf. – volume: 5 start-page: 67 year: 1995 end-page: 93 ident: BIB9 article-title: Factorization of the convection-diffusion operator and the Schwarz algorithm publication-title: Math. Models Methods Appl. Sci. – volume: 1 start-page: 121 year: 1994 end-page: 220 ident: BIB6 article-title: Domain decomposition methods in computational mechanics publication-title: Comput. Mech. Adv. – volume: 2 start-page: 151 year: 1994 end-page: 172 ident: BIB11 article-title: Analysis of a domain-splitting method for nonstationary convection-diffusion problems publication-title: East-West J. Numer. Anal. – year: 1997 ident: BIB2 article-title: A non-overlapping domain decomposition method with adaptive interface conditions for elliptic problems publication-title: Proc. GAMM-Workshop – year: 1997 ident: BIB13 article-title: Galerkin Finite Element Methods for Parabolic Problems – start-page: 71 year: 1997 ident: 10.1016/S0168-9274(98)00053-1_BIB7 article-title: A non-overlapping domain decomposition method for incompressible flow problems – year: 1997 ident: 10.1016/S0168-9274(98)00053-1_BIB13 – year: 1996 ident: 10.1016/S0168-9274(98)00053-1_BIB1 article-title: A note on domain decomposition of singularly perturbed elliptic problems – volume: 17 start-page: 431 year: 1995 ident: 10.1016/S0168-9274(98)00053-1_BIB8 article-title: Stabilized finite element methods for singularly perturbed parabolic problems publication-title: Appl. Numer. Math. doi: 10.1016/0168-9274(95)00024-O – volume: 1 start-page: 121 year: 1994 ident: 10.1016/S0168-9274(98)00053-1_BIB6 article-title: Domain decomposition methods in computational mechanics publication-title: Comput. Mech. Adv. – start-page: 211 year: 1990 ident: 10.1016/S0168-9274(98)00053-1_BIB5 article-title: Domain decomposition methods for unsteady convection-diffusion problems – volume: 37 start-page: 678 issue: 3 year: 1997 ident: 10.1016/S0168-9274(98)00053-1_BIB3 article-title: An accelerated domain decomposition procedure based on Robin transmission conditions publication-title: BIT doi: 10.1007/BF02510246 – volume: 5 start-page: 67 issue: 1 year: 1995 ident: 10.1016/S0168-9274(98)00053-1_BIB9 article-title: Factorization of the convection-diffusion operator and the Schwarz algorithm publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S021820259500005X – volume: 4 start-page: 165 issue: 3 year: 1996 ident: 10.1016/S0168-9274(98)00053-1_BIB4 article-title: Adaptive domain decomposition methods for advection dominated equations publication-title: East-West J. Numer. Math. – volume: 2 start-page: 151 year: 1994 ident: 10.1016/S0168-9274(98)00053-1_BIB11 article-title: Analysis of a domain-splitting method for nonstationary convection-diffusion problems publication-title: East-West J. Numer. Anal. – volume: 87 start-page: 35 year: 1991 ident: 10.1016/S0168-9274(98)00053-1_BIB12 article-title: A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(91)90145-V – year: 1997 ident: 10.1016/S0168-9274(98)00053-1_BIB2 article-title: A non-overlapping domain decomposition method with adaptive interface conditions for elliptic problems – year: 1998 ident: 10.1016/S0168-9274(98)00053-1_BIB10 article-title: A non-overlapping domain decomposition method for the Oseen equations publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202598000500 |
| SSID | ssj0005540 |
| Score | 1.5543638 |
| Snippet | A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from... |
| SourceID | pascalfrancis crossref elsevier |
| SourceType | Index Database Enrichment Source Publisher |
| StartPage | 359 |
| SubjectTerms | Advection-reaction-diffusion Exact sciences and technology Mathematics Non-overlapping domain decomposition method Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use |
| Title | A non-overlapping domain decomposition method for parabolic initial-boundary value problems |
| URI | https://dx.doi.org/10.1016/S0168-9274(98)00053-1 |
| Volume | 28 |
| WOSCitedRecordID | wos000076563000018&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: ScienceDirect Freedom Collection customDbUrl: eissn: 1873-5460 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005540 issn: 0168-9274 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1da9swFBVZu4eVQbeuo-3WoYcNNoK7WLId6TEtHd1IP2ApBPZgZMmGgpuGJC0d7Mfv6sOSm26EPezFGAdbwfdYOpLOvQeh97wSAr4xEamMVlHCyn5UCAZnulhd1WNlrzBFXIf9szM2HvOLTudXkwtzV_cnE3Z_z6f_NdRwDYKtU2f_Idz-oXABziHocISww_Fx4P84_jTMcnJrt2Pq7rUvzjpvY2TQhcl_pEWctZiaxCl1cy2MPlZLzZ2ey7lMG0GirhRe6FLC3SutOhJ1VBhfptnPri4brrOujEGNZ-rDy0Ojt_QWXuej0blhzAdhgfZUb9fzo-HQyjJOwlKEyc1rRG1ufcwN5u3lygy6U2J9eJr-lrAWrojL8bHdJ3XVwe1ITK2Jy6NO3q43fPcPByrO2Qdi7E9pFIeRrdnNXxrwvAxRW2yzjD9B64RmDKbu64Ovx-NvQSKUmoRa31DIAPscWv_I2SfX8t-4zfOpmEOwK2uV0uIvoxdoO2R24guPmZeoU0620KYDDHYd_XwLbZwGxLxCPwZ4CSjYAgU_AAq2QMEAFOyBgpeBgg1QcAOUbXT55Xh0dBI5V45IUpotIqISKRVNK14pWhFKY5XBe6hUT-qkZphfpwVnNCZKApfsl4pLmcE8DubVaSxIQV-jNfjP5Q7CsdD8nqUkpWXC4wK4MymSElgoTxPFi12UNO8zl65kvXZOqfOWNjFjuQ5DzlluwpDHu-jA3za1NVtW3cCaYOWOeFpCmQPkVt26_yC4oUGLrb0Vv79Bz8KX9BatLWa35T56Ku8WV_PZOwfI333Mpik |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Applied+numerical+mathematics&rft.atitle=A+non-overlapping+domain+decomposition+method+for+parabolic+initial-boundary+value+problems&rft.au=LUBE%2C+G&rft.au=OTTO%2C+F.+C&rft.au=M%C3%9CLLER%2C+H&rft.date=1998-10-01&rft.pub=Elsevier&rft.issn=0168-9274&rft.volume=28&rft.issue=2-4&rft.spage=359&rft.epage=369&rft_id=info:doi/10.1016%2FS0168-9274%2898%2900053-1&rft.externalDBID=n%2Fa&rft.externalDocID=1603869 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-9274&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-9274&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-9274&client=summon |