Davydov, O. and Sablonniere, P. (2010) C2 piecewise cubic quasiinterpolants on a 6direction mesh. Journal of Approximation Theory, 162 (3). pp. 528544. ISSN 00219045

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Abstract
We study two kinds of quasiinterpolants (abbr. QI) in the space of C2 piecewise cubics in the plane, or in a rectangular domain, endowed with the highly symmetric triangulation generated by a uniform 6direction mesh. It has been proved recently that this space is generated by the integer translates of two multibox splines. One kind of QIs is of differential type and the other of discrete type. As those QIs are exact on the space of cubic polynomials, their approximation order is 4 for sufficiently smooth functions. In addition, they exhibit nice superconvergent properties at some specific points. Moreover, the infinite norms of the discrete QIs being small, they give excellent approximations of a smooth function and of its first order partial derivatives. The approximation properties of the QIs are illustrated by numerical examples.
Item type:  Article 

ID code:  20210 
Keywords:  bivariate splines, quasiinterpolation, 6direction mesh, Mathematics, Analysis, Applied Mathematics, Mathematics(all), Numerical Analysis 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  09 Jun 2010 11:49 
Last modified:  21 May 2015 12:47 
URI:  http://strathprints.strath.ac.uk/id/eprint/20210 
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