Weighted extended B-spline method for the approximation of the stationary Stokes problem

Authors:
V. V. K. Srinivas Kumar;B. V. Rathish Kumar;P. C. Das
Affiliations:
Department of Mathematics, Indian Institute of Science, Yeswantpur, Bangalore, India;Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India;Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 4
Cited 1

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Mixed and hybrid finite element methods
Error estimates for the web-Spline method

Mathematical Methods for Curves and Surfaces
Weighted Extended B-Spline Approximation of Dirichlet Problems

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Abstract

A new stabilized, mesh-free method for the approximation of the Stokes problem, using weighted extended B-splines (WEB-splines) as shape functions has been proposed. The web-spline based bilinear velocity-constant pressure element satisfies the so called inf-sup condition or Ladyshenskaya-Babuška-Brezzi (LBB) condition. The main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular partitions of domain, thus eliminating the difficult and time consuming pre-processing step. Convergence and Condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions.