P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such process numerically. In this paper we introduce a FEHMM scheme...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Yim, Jaeryun Sheen, Dongwoo Sim, Imbo |
| description | A homogenization approach is one of effective strategies to solve multiscale
elliptic problems approximately. The finite element heterogeneous multiscale
method (FEHMM) which is based on the finite element makes possible to simulate
such process numerically. In this paper we introduce a FEHMM scheme for
multiscale elliptic problems based on nonconforming spaces. In particular we
use the noconforming element with the periodic boundary condition introduced in
the companion paper. Theoretical analysis derives a priori error estimates in
the standard Sobolev norms. Several numerical results which confirm our
analysis are provided. |
| doi_str_mv | 10.48550/arxiv.2201.10661 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2201_10661</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2201_10661</sourcerecordid><originalsourceid>FETCH-LOGICAL-a671-b93ab376b88777fcbf2fb065c92b0143f7849774ddfc23101866a974c244aa4e3</originalsourceid><addsrcrecordid>eNpVkLtOwzAYhbMwoMIDMPEPrAl24sYJW6laWqmFIrpHf3xpLbl25DhcnocXpS0sTEc6w_l0viS5oSRj1XhM7jF8mvcszwnNKClLepl8bxp6l6bP3gnvtA8H43bwOqAMxmJUAS3MjTNRwcyqg3IR3joUCj5M3MNGBeOlEfDoBycxfMHUO2mi8a5_gA2GCMtlBpOus0bgqYboIe4V_Oct1JHkd8opP_SwHmw0vUCrYK3i3sur5EKj7dX1X46S7Xy2nS7S1cvTcjpZpVhymrZ1gW3By7aqOOdatDrXLSnHos5bQlmhecVqzpmUWuQFJbQqS6w5EzljiEwVo-T2d_ZsqemCORwvNSdbzdlW8QMC0meZ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method</title><source>arXiv.org</source><creator>Yim, Jaeryun ; Sheen, Dongwoo ; Sim, Imbo</creator><creatorcontrib>Yim, Jaeryun ; Sheen, Dongwoo ; Sim, Imbo</creatorcontrib><description>A homogenization approach is one of effective strategies to solve multiscale
elliptic problems approximately. The finite element heterogeneous multiscale
method (FEHMM) which is based on the finite element makes possible to simulate
such process numerically. In this paper we introduce a FEHMM scheme for
multiscale elliptic problems based on nonconforming spaces. In particular we
use the noconforming element with the periodic boundary condition introduced in
the companion paper. Theoretical analysis derives a priori error estimates in
the standard Sobolev norms. Several numerical results which confirm our
analysis are provided.</description><identifier>DOI: 10.48550/arxiv.2201.10661</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2022-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2201.10661$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2201.10661$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Yim, Jaeryun</creatorcontrib><creatorcontrib>Sheen, Dongwoo</creatorcontrib><creatorcontrib>Sim, Imbo</creatorcontrib><title>P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method</title><description>A homogenization approach is one of effective strategies to solve multiscale
elliptic problems approximately. The finite element heterogeneous multiscale
method (FEHMM) which is based on the finite element makes possible to simulate
such process numerically. In this paper we introduce a FEHMM scheme for
multiscale elliptic problems based on nonconforming spaces. In particular we
use the noconforming element with the periodic boundary condition introduced in
the companion paper. Theoretical analysis derives a priori error estimates in
the standard Sobolev norms. Several numerical results which confirm our
analysis are provided.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpVkLtOwzAYhbMwoMIDMPEPrAl24sYJW6laWqmFIrpHf3xpLbl25DhcnocXpS0sTEc6w_l0viS5oSRj1XhM7jF8mvcszwnNKClLepl8bxp6l6bP3gnvtA8H43bwOqAMxmJUAS3MjTNRwcyqg3IR3joUCj5M3MNGBeOlEfDoBycxfMHUO2mi8a5_gA2GCMtlBpOus0bgqYboIe4V_Oct1JHkd8opP_SwHmw0vUCrYK3i3sur5EKj7dX1X46S7Xy2nS7S1cvTcjpZpVhymrZ1gW3By7aqOOdatDrXLSnHos5bQlmhecVqzpmUWuQFJbQqS6w5EzljiEwVo-T2d_ZsqemCORwvNSdbzdlW8QMC0meZ</recordid><startdate>20220125</startdate><enddate>20220125</enddate><creator>Yim, Jaeryun</creator><creator>Sheen, Dongwoo</creator><creator>Sim, Imbo</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220125</creationdate><title>P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method</title><author>Yim, Jaeryun ; Sheen, Dongwoo ; Sim, Imbo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-b93ab376b88777fcbf2fb065c92b0143f7849774ddfc23101866a974c244aa4e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Yim, Jaeryun</creatorcontrib><creatorcontrib>Sheen, Dongwoo</creatorcontrib><creatorcontrib>Sim, Imbo</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yim, Jaeryun</au><au>Sheen, Dongwoo</au><au>Sim, Imbo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method</atitle><date>2022-01-25</date><risdate>2022</risdate><abstract>A homogenization approach is one of effective strategies to solve multiscale
elliptic problems approximately. The finite element heterogeneous multiscale
method (FEHMM) which is based on the finite element makes possible to simulate
such process numerically. In this paper we introduce a FEHMM scheme for
multiscale elliptic problems based on nonconforming spaces. In particular we
use the noconforming element with the periodic boundary condition introduced in
the companion paper. Theoretical analysis derives a priori error estimates in
the standard Sobolev norms. Several numerical results which confirm our
analysis are provided.</abstract><doi>10.48550/arxiv.2201.10661</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2201.10661 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2201_10661 |
| source | arXiv.org |
| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | P_1$--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T13%3A09%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=P_1$--Nonconforming%20Quadrilateral%20Finite%20Element%20Space%20with%20Periodic%20Boundary%20Conditions:%20Part%20II.%20Application%20to%20the%20Nonconforming%20Heterogeneous%20Multiscale%20Method&rft.au=Yim,%20Jaeryun&rft.date=2022-01-25&rft_id=info:doi/10.48550/arxiv.2201.10661&rft_dat=%3Carxiv_GOX%3E2201_10661%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |