Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure
We consider a second-order elliptic operator A=A( x )=−∑ i,j=1 d ∂ ia ij( x ) ∂ j+∑ j=1 db j′( x ) ∂ j+∑ j=1 d ∂ j(b j″( x )·)+c( x ) on R d from the point of view of its numerical approximations in terms of matrices A n having compartmental structure, that is ( A n ) ii >0, ( A n ) ij ⩽0, i≠ j,...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2004-03, Vol.164 (Complete), p.493-516 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Limić, Nedžad Rogina, Mladen |
| description | We consider a second-order elliptic operator
A=A(
x
)=−∑
i,j=1
d
∂
ia
ij(
x
)
∂
j+∑
j=1
db
j′(
x
)
∂
j+∑
j=1
d
∂
j(b
j″(
x
)·)+c(
x
)
on
R
d
from the point of view of its numerical approximations in terms of matrices
A
n
having compartmental structure, that is (
A
n
)
ii
>0, (
A
n
)
ij
⩽0,
i≠
j, ∑
i
(
A
n
)
ij
⩾0. We solve numerically the corresponding Dirichlet problem on a bounded domain
D⊂
R
d(d=2,3)
, for which the right-hand side is a probability measure with support in
D. Numerical solutions on grids are nonpositive, and can be naturally embedded into linear spaces of ‘hat’ functions approximating the original solution in
W
̇
1
1(D)
. Numerical solutions converge in
L
1(
D).
The construction of our approximations is valid for general dimensions, but we give the convergence proof only for
d=2,3. We end by a nontrivial example that illustrates the obtained results. |
| doi_str_mv | 10.1016/S0377-0427(03)00649-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_28269370</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042703006496</els_id><sourcerecordid>28269370</sourcerecordid><originalsourceid>FETCH-LOGICAL-c385t-d65369c032e8c9dfbfe4b57267c9c106a9971e95fd41773a4d60cc2eabde349b3</originalsourceid><addsrcrecordid>eNqFkE1LxTAQRYMo-Pz4CUJWootq0rRJsxLxG0QX6jqkydQXaZuapIr_3jyfuHU1MJw7zD0IHVByQgnlp0-ECVGQqhRHhB0TwitZ8A20oI2QBRWi2USLP2Qb7cT4RjIlabVA08M8QHBG9zj6fk7OjxH7Dl-6vFz2kPAUfNvDgDsfMPS9m5Iz2E8QdMobN2LrPiC8wmhgxQz406Ul1ji412Uqlnq0ODoLeAAd5wB7aKvTfYT937mLXq6vni9ui_vHm7uL8_vCsKZOheU149IQVkJjpO3aDqq2FiUXRhpKuJZSUJB1Z6vckOnKcmJMCbq1wCrZsl10uL6b_3-fISY1uGhyAT2Cn6Mqm5JLJkgG6zVogo8xQKem4AYdvhQlauVX_fhVK3mKMPXjV_GcO1vnILf4cBBUNG5lwboAJinr3T8XvgHnBISj</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>28269370</pqid></control><display><type>article</type><title>Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Access via ScienceDirect (Elsevier)</source><creator>Limić, Nedžad ; Rogina, Mladen</creator><creatorcontrib>Limić, Nedžad ; Rogina, Mladen</creatorcontrib><description>We consider a second-order elliptic operator
A=A(
x
)=−∑
i,j=1
d
∂
ia
ij(
x
)
∂
j+∑
j=1
db
j′(
x
)
∂
j+∑
j=1
d
∂
j(b
j″(
x
)·)+c(
x
)
on
R
d
from the point of view of its numerical approximations in terms of matrices
A
n
having compartmental structure, that is (
A
n
)
ii
>0, (
A
n
)
ij
⩽0,
i≠
j, ∑
i
(
A
n
)
ij
⩾0. We solve numerically the corresponding Dirichlet problem on a bounded domain
D⊂
R
d(d=2,3)
, for which the right-hand side is a probability measure with support in
D. Numerical solutions on grids are nonpositive, and can be naturally embedded into linear spaces of ‘hat’ functions approximating the original solution in
W
̇
1
1(D)
. Numerical solutions converge in
L
1(
D).
The construction of our approximations is valid for general dimensions, but we give the convergence proof only for
d=2,3. We end by a nontrivial example that illustrates the obtained results.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/S0377-0427(03)00649-6</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Difference scheme ; Divergence form ; Elliptic operator</subject><ispartof>Journal of computational and applied mathematics, 2004-03, Vol.164 (Complete), p.493-516</ispartof><rights>2003</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c385t-d65369c032e8c9dfbfe4b57267c9c106a9971e95fd41773a4d60cc2eabde349b3</citedby><cites>FETCH-LOGICAL-c385t-d65369c032e8c9dfbfe4b57267c9c106a9971e95fd41773a4d60cc2eabde349b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/S0377-0427(03)00649-6$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Limić, Nedžad</creatorcontrib><creatorcontrib>Rogina, Mladen</creatorcontrib><title>Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure</title><title>Journal of computational and applied mathematics</title><description>We consider a second-order elliptic operator
A=A(
x
)=−∑
i,j=1
d
∂
ia
ij(
x
)
∂
j+∑
j=1
db
j′(
x
)
∂
j+∑
j=1
d
∂
j(b
j″(
x
)·)+c(
x
)
on
R
d
from the point of view of its numerical approximations in terms of matrices
A
n
having compartmental structure, that is (
A
n
)
ii
>0, (
A
n
)
ij
⩽0,
i≠
j, ∑
i
(
A
n
)
ij
⩾0. We solve numerically the corresponding Dirichlet problem on a bounded domain
D⊂
R
d(d=2,3)
, for which the right-hand side is a probability measure with support in
D. Numerical solutions on grids are nonpositive, and can be naturally embedded into linear spaces of ‘hat’ functions approximating the original solution in
W
̇
1
1(D)
. Numerical solutions converge in
L
1(
D).
The construction of our approximations is valid for general dimensions, but we give the convergence proof only for
d=2,3. We end by a nontrivial example that illustrates the obtained results.</description><subject>Difference scheme</subject><subject>Divergence form</subject><subject>Elliptic operator</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNqFkE1LxTAQRYMo-Pz4CUJWootq0rRJsxLxG0QX6jqkydQXaZuapIr_3jyfuHU1MJw7zD0IHVByQgnlp0-ECVGQqhRHhB0TwitZ8A20oI2QBRWi2USLP2Qb7cT4RjIlabVA08M8QHBG9zj6fk7OjxH7Dl-6vFz2kPAUfNvDgDsfMPS9m5Iz2E8QdMobN2LrPiC8wmhgxQz406Ul1ji412Uqlnq0ODoLeAAd5wB7aKvTfYT937mLXq6vni9ui_vHm7uL8_vCsKZOheU149IQVkJjpO3aDqq2FiUXRhpKuJZSUJB1Z6vckOnKcmJMCbq1wCrZsl10uL6b_3-fISY1uGhyAT2Cn6Mqm5JLJkgG6zVogo8xQKem4AYdvhQlauVX_fhVK3mKMPXjV_GcO1vnILf4cBBUNG5lwboAJinr3T8XvgHnBISj</recordid><startdate>20040301</startdate><enddate>20040301</enddate><creator>Limić, Nedžad</creator><creator>Rogina, Mladen</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20040301</creationdate><title>Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure</title><author>Limić, Nedžad ; Rogina, Mladen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c385t-d65369c032e8c9dfbfe4b57267c9c106a9971e95fd41773a4d60cc2eabde349b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Difference scheme</topic><topic>Divergence form</topic><topic>Elliptic operator</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Limić, Nedžad</creatorcontrib><creatorcontrib>Rogina, Mladen</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Limić, Nedžad</au><au>Rogina, Mladen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2004-03-01</date><risdate>2004</risdate><volume>164</volume><issue>Complete</issue><spage>493</spage><epage>516</epage><pages>493-516</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>We consider a second-order elliptic operator
A=A(
x
)=−∑
i,j=1
d
∂
ia
ij(
x
)
∂
j+∑
j=1
db
j′(
x
)
∂
j+∑
j=1
d
∂
j(b
j″(
x
)·)+c(
x
)
on
R
d
from the point of view of its numerical approximations in terms of matrices
A
n
having compartmental structure, that is (
A
n
)
ii
>0, (
A
n
)
ij
⩽0,
i≠
j, ∑
i
(
A
n
)
ij
⩾0. We solve numerically the corresponding Dirichlet problem on a bounded domain
D⊂
R
d(d=2,3)
, for which the right-hand side is a probability measure with support in
D. Numerical solutions on grids are nonpositive, and can be naturally embedded into linear spaces of ‘hat’ functions approximating the original solution in
W
̇
1
1(D)
. Numerical solutions converge in
L
1(
D).
The construction of our approximations is valid for general dimensions, but we give the convergence proof only for
d=2,3. We end by a nontrivial example that illustrates the obtained results.</abstract><pub>Elsevier B.V</pub><doi>10.1016/S0377-0427(03)00649-6</doi><tpages>24</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2004-03, Vol.164 (Complete), p.493-516 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28269370 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Access via ScienceDirect (Elsevier) |
| subjects | Difference scheme Divergence form Elliptic operator |
| title | Numerical solutions of Dirichlet problem for elliptic operator in divergence form with a right-hand side measure |
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