A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations
An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form ∑ i = 1 ℓ q i ( t ) D t α i u ( x , t ) , where the q i are continuous functions, each D t α i is a Caputo derivative, and the α i lie in (0, 1]. Maximum/comparison...
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| Veröffentlicht in: | Journal of scientific computing 2022-08, Vol.92 (2), p.73, Article 73 |
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| creator | Kopteva, Natalia Stynes, Martin |
| description | An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form
∑
i
=
1
ℓ
q
i
(
t
)
D
t
α
i
u
(
x
,
t
)
, where the
q
i
are continuous functions, each
D
t
α
i
is a Caputo derivative, and the
α
i
lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in
L
2
(
Ω
)
and
L
∞
(
Ω
)
, where the spatial domain
Ω
lies in
R
d
with
d
∈
{
1
,
2
,
3
}
. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm. |
| doi_str_mv | 10.1007/s10915-022-01936-2 |
| format | Article |
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∑
i
=
1
ℓ
q
i
(
t
)
D
t
α
i
u
(
x
,
t
)
, where the
q
i
are continuous functions, each
D
t
α
i
is a Caputo derivative, and the
α
i
lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in
L
2
(
Ω
)
and
L
∞
(
Ω
)
, where the spatial domain
Ω
lies in
R
d
with
d
∈
{
1
,
2
,
3
}
. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-022-01936-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Adaptive algorithms ; Algorithms ; Aquifers ; Boundary value problems ; Computational Mathematics and Numerical Analysis ; Continuity (mathematics) ; Differential equations ; Error analysis ; Hypotheses ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Numerical analysis ; Operators (mathematics) ; Theoretical</subject><ispartof>Journal of scientific computing, 2022-08, Vol.92 (2), p.73, Article 73</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-61fe567a53b448f255a033f0cbfbe5a6cf54a2cdf7736a1dfb5ee00fecea63943</citedby><cites>FETCH-LOGICAL-c319t-61fe567a53b448f255a033f0cbfbe5a6cf54a2cdf7736a1dfb5ee00fecea63943</cites><orcidid>0000-0001-7477-6926 ; 0000-0003-2085-7354</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-022-01936-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918315607?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72341</link.rule.ids></links><search><creatorcontrib>Kopteva, Natalia</creatorcontrib><creatorcontrib>Stynes, Martin</creatorcontrib><title>A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form
∑
i
=
1
ℓ
q
i
(
t
)
D
t
α
i
u
(
x
,
t
)
, where the
q
i
are continuous functions, each
D
t
α
i
is a Caputo derivative, and the
α
i
lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in
L
2
(
Ω
)
and
L
∞
(
Ω
)
, where the spatial domain
Ω
lies in
R
d
with
d
∈
{
1
,
2
,
3
}
. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.</description><subject>Adaptive algorithms</subject><subject>Algorithms</subject><subject>Aquifers</subject><subject>Boundary value problems</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Continuity (mathematics)</subject><subject>Differential equations</subject><subject>Error analysis</subject><subject>Hypotheses</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><subject>Operators (mathematics)</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPAczQfm2RzLKVVoaJg9Rqy6URStt022T3035tawZun4R3eZxgehG4ZvWeU6ofMqGGSUM4JZUYows_QiEktiFaGnaMRrWtJdKWrS3SV85pSamrDRwgm-K3LPaTYpYhnKXUJT7auPeSYcSjh06XomhbItIMQoo-w7fHL0PaxQBu8jBsg8-R8H7uC4fehWcUQhlwinu0Hd9zna3QRXJvh5neO0cd8tpw-kcXr4_N0siBeMNMTxQJIpZ0UTVXVgUvpqBCB-iY0IJ3yQVaO-1XQWijHVqGRAJQG8OCUMJUYo7vT3V3q9gPk3q67IZW_suWG1YJJRXVp8VPLpy7nBMHuUty4dLCM2qNOe9Jpi077o9PyAokTlEt5-wXp7_Q_1DeG9Hov</recordid><startdate>20220801</startdate><enddate>20220801</enddate><creator>Kopteva, Natalia</creator><creator>Stynes, Martin</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><orcidid>https://orcid.org/0000-0001-7477-6926</orcidid><orcidid>https://orcid.org/0000-0003-2085-7354</orcidid></search><sort><creationdate>20220801</creationdate><title>A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations</title><author>Kopteva, Natalia ; Stynes, Martin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-61fe567a53b448f255a033f0cbfbe5a6cf54a2cdf7736a1dfb5ee00fecea63943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Adaptive algorithms</topic><topic>Algorithms</topic><topic>Aquifers</topic><topic>Boundary value problems</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Continuity (mathematics)</topic><topic>Differential equations</topic><topic>Error analysis</topic><topic>Hypotheses</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><topic>Operators (mathematics)</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kopteva, Natalia</creatorcontrib><creatorcontrib>Stynes, Martin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & 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 & Aerospace Database</collection><collection>ProQuest Advanced Technologies & 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>Kopteva, Natalia</au><au>Stynes, Martin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2022-08-01</date><risdate>2022</risdate><volume>92</volume><issue>2</issue><spage>73</spage><pages>73-</pages><artnum>73</artnum><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form
∑
i
=
1
ℓ
q
i
(
t
)
D
t
α
i
u
(
x
,
t
)
, where the
q
i
are continuous functions, each
D
t
α
i
is a Caputo derivative, and the
α
i
lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in
L
2
(
Ω
)
and
L
∞
(
Ω
)
, where the spatial domain
Ω
lies in
R
d
with
d
∈
{
1
,
2
,
3
}
. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-022-01936-2</doi><orcidid>https://orcid.org/0000-0001-7477-6926</orcidid><orcidid>https://orcid.org/0000-0003-2085-7354</orcidid></addata></record> |
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| language | eng |
| recordid | cdi_proquest_journals_2918315607 |
| source | ProQuest Central UK/Ireland; SpringerLink Journals - AutoHoldings; ProQuest Central |
| subjects | Adaptive algorithms Algorithms Aquifers Boundary value problems Computational Mathematics and Numerical Analysis Continuity (mathematics) Differential equations Error analysis Hypotheses Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Numerical analysis Operators (mathematics) Theoretical |
| title | A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations |
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