Compatible convergence estimates in the method of refinement by higher-order differences
We consider the Dirichlet problem for an elliptic equation with constant coefficients, which is solved by a difference scheme of second-order accuracy. By using the approximate solution, we correct the right-hand side of the difference scheme. We show that the solution of the corrected scheme is con...
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| Veröffentlicht in: | Differential equations 2015, Vol.51 (1), p.107-115 |
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| container_title | Differential equations |
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| creator | Berikelashvili, G. K. Midodashvili, B. G. |
| description | We consider the Dirichlet problem for an elliptic equation with constant coefficients, which is solved by a difference scheme of second-order accuracy. By using the approximate solution, we correct the right-hand side of the difference scheme. We show that the solution of the corrected scheme is convergent at the rate
O
(|
h
|
m
) in the discrete
L
2
-norm provided that the solution of the original problem belongs to the Sobolev space with exponent
m
∈ [2, 4]. |
| doi_str_mv | 10.1134/S0012266115010103 |
| format | Article |
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O
(|
h
|
m
) in the discrete
L
2
-norm provided that the solution of the original problem belongs to the Sobolev space with exponent
m
∈ [2, 4].</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266115010103</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Accuracy ; Approximation ; Boundary conditions ; Compatibility ; Constants ; Convergence ; Difference and Functional Equations ; Differential equations ; Dirichlet problem ; Estimates ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Norms ; Numerical Methods ; Ordinary Differential Equations ; Partial Differential Equations ; Sobolev space ; Studies</subject><ispartof>Differential equations, 2015, Vol.51 (1), p.107-115</ispartof><rights>Pleiades Publishing, Ltd. 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-5b7a2af6f21d79b41649ef96be0669459cb9438b73eb9b5b710b8396b874c4a93</citedby><cites>FETCH-LOGICAL-c349t-5b7a2af6f21d79b41649ef96be0669459cb9438b73eb9b5b710b8396b874c4a93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266115010103$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266115010103$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Berikelashvili, G. K.</creatorcontrib><creatorcontrib>Midodashvili, B. G.</creatorcontrib><title>Compatible convergence estimates in the method of refinement by higher-order differences</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We consider the Dirichlet problem for an elliptic equation with constant coefficients, which is solved by a difference scheme of second-order accuracy. By using the approximate solution, we correct the right-hand side of the difference scheme. We show that the solution of the corrected scheme is convergent at the rate
O
(|
h
|
m
) in the discrete
L
2
-norm provided that the solution of the original problem belongs to the Sobolev space with exponent
m
∈ [2, 4].</description><subject>Accuracy</subject><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Compatibility</subject><subject>Constants</subject><subject>Convergence</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Dirichlet problem</subject><subject>Estimates</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Numerical Methods</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Sobolev space</subject><subject>Studies</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kE9LxDAQxYMouK5-AG8BL16qmSZNk6Ms_gPBgwreStNOtl22yZp0hf32pqwHUWQOc3i_95h5hJwDuwLg4vqFMchzKQEKBmn4AZmBZCrjTPFDMpvkbNKPyUmMK8aYLqGYkfeFHzb12Js10sa7TwxLdA1SjGM_1CNG2js6dkgHHDvfUm9pQNs7HNCN1Oxo1y87DJkPLQba9tZimALiKTmy9Tri2feek7e729fFQ_b0fP-4uHnKGi70mBWmrPPaSptDW2ojQAqNVkuDTEotCt0YLbgyJUejTaKBGcWTrkrRiFrzObnc526C_9ims6uhjw2u17VDv40VpBhVFCkpoRe_0JXfBpeuS1QhVKl4LhMFe6oJPsb0bLUJqYqwq4BVU9fVn66TJ997YmLdEsOP5H9NXxmGf6Y</recordid><startdate>2015</startdate><enddate>2015</enddate><creator>Berikelashvili, G. 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O
(|
h
|
m
) in the discrete
L
2
-norm provided that the solution of the original problem belongs to the Sobolev space with exponent
m
∈ [2, 4].</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266115010103</doi><tpages>9</tpages></addata></record> |
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| ispartof | Differential equations, 2015, Vol.51 (1), p.107-115 |
| issn | 0012-2661 1608-3083 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Accuracy Approximation Boundary conditions Compatibility Constants Convergence Difference and Functional Equations Differential equations Dirichlet problem Estimates Mathematical analysis Mathematics Mathematics and Statistics Norms Numerical Methods Ordinary Differential Equations Partial Differential Equations Sobolev space Studies |
| title | Compatible convergence estimates in the method of refinement by higher-order differences |
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