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


High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

Renzhong Feng 1*

1 School of Mathematics and Systematic Science & Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing University of Aeronautics and Astronautics, Beijing 100191, China.

Received 20 December 2010; Accepted (in revised version) 25 February 2012
Available online 11 June 2012
doi:10.4208/cicp.201210.250212a

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.

AMS subject classifications: 65M99, 82D37, 82-08

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Key words: Cubic-Polynomial Interpolation scheme, hyperbolic equations, triangular mesh.

*Corresponding author.
Email: fengrz@buaa.edu.cn (R. Feng)
 

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