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On the Dimension of Bivariate Weak Spline Space Over Regular Rectilinear Partition

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Abstract

In this paper, we mainly study the dimensions of bivariate weak spline spaces \({W_k^\mu(I_{1}\Delta)}\) (k ≥ 2μ+1) and \({W_{2}^{1} (I_{1}^{*}\Delta)}\) by using the smoothing cofactor-conformality method, where I 1Δ and \({I_{1}^{*} \Delta}\) are regular rectilinear partitions with appointed point sets. Some future works relative to bivariate weak splines are also listed at the end of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, 266071, Qingdao, Shandong, China

    Feng-Gong Lang

  2. Institute of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, Liaoning, China

    Ren-Hong Wang

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  1. Feng-Gong Lang
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  2. Ren-Hong Wang
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Correspondence to Feng-Gong Lang.

Additional information

Project was supported by the National Natural Science Foundation of China (No.60533060).

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Lang, FG., Wang, RH. On the Dimension of Bivariate Weak Spline Space Over Regular Rectilinear Partition. Results. Math. 57, 79–95 (2010). https://doi.org/10.1007/s00025-009-0003-y

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  • DOI: https://doi.org/10.1007/s00025-009-0003-y

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