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Volume 12, Issue 5
High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

Renzhong Feng

DOI: 10.4208/cicp.201210.250212a

Commun. Comput. Phys., 12 (2012), pp. 1588-1602.

Published online: 2012-12

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  • Abstract

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes. 

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@Article{CiCP-12-1588, author = {Renzhong Feng}, title = {High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {1588--1602}, abstract = {

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.201210.250212a}, url = {http://global-sci.org/intro/article_detail/cicp/7348.html} }
TY - JOUR T1 - High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes AU - Renzhong Feng JO - Communications in Computational Physics VL - 5 SP - 1588 EP - 1602 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.201210.250212a UR - https://global-sci.org/intro/article_detail/cicp/7348.html KW - AB -

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes. 

Renzhong Feng. (2012). High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes. Communications in Computational Physics. 12 (5). 1588-1602. doi:10.4208/cicp.201210.250212a
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