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Volume 9, Issue 4
Second Order Convergence of the Interpolation Based on $Q^c_1$-Element

Ruijian He & Xinlong Feng

DOI: 10.4208/nmtma.2016.m1503

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 595-618.

Published online: 2016-09

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  • Abstract

In this paper, the second order convergence of the interpolation based on $Q^c_1$-element is derived in the case of $d$=1, 2 and 3. Using the integral average on each element, the new basis functions of tensor product type is builded up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.

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@Article{NMTMA-9-595, author = {Ruijian He and Xinlong Feng}, title = {Second Order Convergence of the Interpolation Based on $Q^c_1$-Element}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {4}, pages = {595--618}, abstract = {

In this paper, the second order convergence of the interpolation based on $Q^c_1$-element is derived in the case of $d$=1, 2 and 3. Using the integral average on each element, the new basis functions of tensor product type is builded up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1503}, url = {http://global-sci.org/intro/article_detail/nmtma/12391.html} }
TY - JOUR T1 - Second Order Convergence of the Interpolation Based on $Q^c_1$-Element AU - Ruijian He & Xinlong Feng JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 595 EP - 618 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1503 UR - https://global-sci.org/intro/article_detail/nmtma/12391.html KW - AB -

In this paper, the second order convergence of the interpolation based on $Q^c_1$-element is derived in the case of $d$=1, 2 and 3. Using the integral average on each element, the new basis functions of tensor product type is builded up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.

Ruijian He and Xinlong Feng. (2016). Second Order Convergence of the Interpolation Based on $Q^c_1$-Element. Numerical Mathematics: Theory, Methods and Applications. 9 (4). 595-618. doi:10.4208/nmtma.2016.m1503
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