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Volume 30, Issue 5
A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations

Xinping Shao, Danfu Han & Xianliang Hu

DOI: 10.4208/jcm.1203-m3813

J. Comp. Math., 30 (2012), pp. 544-554.

Published online: 2012-10

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  • Abstract

A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implemented in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy is generated subsequently, via one step Newton or modified Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.

  • Keywords

P-version, Two level method, Spline methods, Semi-linear, Error estimation.

  • AMS Subject Headings

65N30, 65M55.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-30-544, author = {Xinping Shao, Danfu Han and Xianliang Hu}, title = {A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {5}, pages = {544--554}, abstract = {

A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implemented in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy is generated subsequently, via one step Newton or modified Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1203-m3813}, url = {http://global-sci.org/intro/article_detail/jcm/8449.html} }
TY - JOUR T1 - A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations AU - Xinping Shao, Danfu Han & Xianliang Hu JO - Journal of Computational Mathematics VL - 5 SP - 544 EP - 554 PY - 2012 DA - 2012/10 SN - 30 DO - http://doi.org/10.4208/jcm.1203-m3813 UR - https://global-sci.org/intro/article_detail/jcm/8449.html KW - P-version, Two level method, Spline methods, Semi-linear, Error estimation. AB -

A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implemented in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy is generated subsequently, via one step Newton or modified Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.

Xinping Shao, Danfu Han and Xianliang Hu. (2012). A P-Version Two Level Spline Method for Semi-Linear Elliptic Equations. Journal of Computational Mathematics. 30 (5). 544-554. doi:10.4208/jcm.1203-m3813
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