A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes

Authors:
Dan Liu;Guoliang Xu;Qin Zhang
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, Chin ...;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, Chin ...;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, Chin ...
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

Laplace-Beltrami operator and its discretization play a central role in the fields of image processing, computer graphics, computer aided geometric design and so on. In this paper, a discrete scheme for Laplace-Beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral. Convergence results for the proposed discrete scheme are established under some conditions. Numerical results which justify the theoretical analysis are also given.