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The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem
In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k , the numerical flux convergence at a rate of 2 k + 2 for all mesh nodes (in particular, the numerical flux for k = 0 has the second order sup...
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| Published in: | Journal of scientific computing 2017, Vol.70 (1), p.175-191 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c316t-a30f413abc865a80c6b4757494c6c4578af01ef807a99d851e70825c0cdab3f73 |
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| cites | cdi_FETCH-LOGICAL-c316t-a30f413abc865a80c6b4757494c6c4578af01ef807a99d851e70825c0cdab3f73 |
| container_end_page | 191 |
| container_issue | 1 |
| container_start_page | 175 |
| container_title | Journal of scientific computing |
| container_volume | 70 |
| creator | Wang, Jiangxing Chen, Chuanmiao Xie, Ziqing |
| description | In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree
k
, the numerical flux convergence at a rate of
2
k
+
2
for all mesh nodes (in particular, the numerical flux for
k
=
0
has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results. |
| doi_str_mv | 10.1007/s10915-016-0247-0 |
| format | article |
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k
, the numerical flux convergence at a rate of
2
k
+
2
for all mesh nodes (in particular, the numerical flux for
k
=
0
has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-016-0247-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Boundary value problems ; Computational Mathematics and Numerical Analysis ; Equality ; Estimates ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Polynomials ; Theoretical</subject><ispartof>Journal of scientific computing, 2017, Vol.70 (1), p.175-191</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Springer Science+Business Media New York 2016.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-a30f413abc865a80c6b4757494c6c4578af01ef807a99d851e70825c0cdab3f73</citedby><cites>FETCH-LOGICAL-c316t-a30f413abc865a80c6b4757494c6c4578af01ef807a99d851e70825c0cdab3f73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27898,27899</link.rule.ids></links><search><creatorcontrib>Wang, Jiangxing</creatorcontrib><creatorcontrib>Chen, Chuanmiao</creatorcontrib><creatorcontrib>Xie, Ziqing</creatorcontrib><title>The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree
k
, the numerical flux convergence at a rate of
2
k
+
2
for all mesh nodes (in particular, the numerical flux for
k
=
0
has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.</description><subject>Algorithms</subject><subject>Boundary value problems</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Equality</subject><subject>Estimates</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Polynomials</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLwzAYhoMoOKc_wFvAc_VLmzTJcU7dBMWBU_AU0jTZOrpmJq2yf29HBU-evsv7vN_Lg9AlgWsCwG8iAUlYAiRPIKU8gSM0IoxnCc8lOUYjEIIlnHJ6is5i3ACAFDIdoY_l2uJ5tVrb2OLXbmeD8c2XDSvbGIsnja73sYrYOzy5m-Fn2659iZ0PePnt8cJXTYtvfdeUOuzxu647G_Ei-KK223N04nQd7cXvHaO3h_vldJ48vcwep5OnxGQkbxOdgaMk04UROdMCTF5QzjiV1OSGMi60A2KdAK6lLAUjloNImQFT6iJzPBujq6F3F_xn_79VG9-FfnhUqSQiI2nKDikypEzwMQbr1C5U2361IqAOBtVgUPUG1cGggp5JByb22WZlw1_z_9APkdpylw</recordid><startdate>2017</startdate><enddate>2017</enddate><creator>Wang, Jiangxing</creator><creator>Chen, Chuanmiao</creator><creator>Xie, Ziqing</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>PHGZM</scope><scope>PHGZT</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>2017</creationdate><title>The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem</title><author>Wang, Jiangxing ; Chen, Chuanmiao ; Xie, Ziqing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-a30f413abc865a80c6b4757494c6c4578af01ef807a99d851e70825c0cdab3f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algorithms</topic><topic>Boundary value problems</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Equality</topic><topic>Estimates</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Methods</topic><topic>Polynomials</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Jiangxing</creatorcontrib><creatorcontrib>Chen, Chuanmiao</creatorcontrib><creatorcontrib>Xie, Ziqing</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 Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied & Life Sciences</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>Wang, Jiangxing</au><au>Chen, Chuanmiao</au><au>Xie, Ziqing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2017</date><risdate>2017</risdate><volume>70</volume><issue>1</issue><spage>175</spage><epage>191</epage><pages>175-191</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree
k
, the numerical flux convergence at a rate of
2
k
+
2
for all mesh nodes (in particular, the numerical flux for
k
=
0
has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-016-0247-0</doi><tpages>17</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0885-7474 |
| ispartof | Journal of scientific computing, 2017, Vol.70 (1), p.175-191 |
| issn | 0885-7474 1573-7691 |
| language | eng |
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| source | Springer Link |
| subjects | Algorithms Boundary value problems Computational Mathematics and Numerical Analysis Equality Estimates Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Polynomials Theoretical |
| title | The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem |
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