Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the m -th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart ( m = 1 ) or Morley ( m = 2 ) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eig...
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| Veröffentlicht in: | Numerische Mathematik 2024-02, Vol.156 (1), p.1-38 |
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| creator | Carstensen, Carsten Puttkammer, Sophie |
| description | Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the
m
-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart (
m
=
1
) or Morley (
m
=
2
) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated
L
2
error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in 3D and highlights a new version of discrete reliability. |
| doi_str_mv | 10.1007/s00211-023-01382-8 |
| format | Article |
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m
-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart (
m
=
1
) or Morley (
m
=
2
) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated
L
2
error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in 3D and highlights a new version of discrete reliability.</description><identifier>ISSN: 0029-599X</identifier><identifier>EISSN: 0945-3245</identifier><identifier>DOI: 10.1007/s00211-023-01382-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Adaptive algorithms ; Axioms ; Convergence ; Dirichlet problem ; Eigenvalues ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Numerical and Computational Physics ; Simulation ; Theoretical</subject><ispartof>Numerische Mathematik, 2024-02, Vol.156 (1), p.1-38</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-cd45f95910c0ef573306d72c8cca5d8ee1aa7d8e35b12ae5c6f54069824079893</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00211-023-01382-8$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00211-023-01382-8$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Carstensen, Carsten</creatorcontrib><creatorcontrib>Puttkammer, Sophie</creatorcontrib><title>Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates</title><title>Numerische Mathematik</title><addtitle>Numer. Math</addtitle><description>Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the
m
-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart (
m
=
1
) or Morley (
m
=
2
) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated
L
2
error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in 3D and highlights a new version of discrete reliability.</description><subject>Adaptive algorithms</subject><subject>Axioms</subject><subject>Convergence</subject><subject>Dirichlet problem</subject><subject>Eigenvalues</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Numerical and Computational Physics</subject><subject>Simulation</subject><subject>Theoretical</subject><issn>0029-599X</issn><issn>0945-3245</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPAc3TytdkcS1GrFLwoeAtpdra2rLs12W3x3xtdwZunmcPzvjM8hFxyuOYA5iYBCM4ZCMmAy1Kw8ohMwCrNpFD6OO8gLNPWvp6Ss5S2ANwUik_I46zyu36zR7oefPRtj1jRpjtgpLhZY7v3zYB01Q1tlehh07_RLuPvvqGha_cYMxKQRt9jOicntW8SXvzOKXm5u32eL9jy6f5hPluyILnqWaiUrq22HAJgrY2UUFRGhDIEr6sSkXtv8pR6xYVHHYpaKyhsKRQYW1o5JVdj7y52HwOm3m27Ibb5pBNWcCO1EjJTYqRC7FKKWLtdzH_HT8fBfTtzozOXnbkfZ67MITmGUobbNca_6n9SX9V0b0o</recordid><startdate>20240201</startdate><enddate>20240201</enddate><creator>Carstensen, Carsten</creator><creator>Puttkammer, Sophie</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240201</creationdate><title>Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates</title><author>Carstensen, Carsten ; Puttkammer, Sophie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-cd45f95910c0ef573306d72c8cca5d8ee1aa7d8e35b12ae5c6f54069824079893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Adaptive algorithms</topic><topic>Axioms</topic><topic>Convergence</topic><topic>Dirichlet problem</topic><topic>Eigenvalues</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Numerical and Computational Physics</topic><topic>Simulation</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carstensen, Carsten</creatorcontrib><creatorcontrib>Puttkammer, Sophie</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Numerische Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carstensen, Carsten</au><au>Puttkammer, Sophie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates</atitle><jtitle>Numerische Mathematik</jtitle><stitle>Numer. Math</stitle><date>2024-02-01</date><risdate>2024</risdate><volume>156</volume><issue>1</issue><spage>1</spage><epage>38</epage><pages>1-38</pages><issn>0029-599X</issn><eissn>0945-3245</eissn><abstract>Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the
m
-th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix–Raviart (
m
=
1
) or Morley (
m
=
2
) finite element eigensolver. Striking numerical evidence for the superiority of a new adaptive eigensolver motivates the convergence analysis in this paper with a proof of optimal convergence rates of the GLB towards a simple eigenvalue. The proof is based on (a generalization of) known abstract arguments entitled as the axioms of adaptivity. Beyond the known a priori convergence rates, a medius analysis is enfolded in this paper for the proof of best-approximation results. This and subordinated
L
2
error estimates for locally refined triangulations appear of independent interest. The analysis of optimal convergence rates of an adaptive mesh-refining algorithm is performed in 3D and highlights a new version of discrete reliability.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00211-023-01382-8</doi><tpages>38</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Adaptive algorithms Axioms Convergence Dirichlet problem Eigenvalues Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical and Computational Physics Simulation Theoretical |
| title | Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates |
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