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Keywords:

  • mesh-free methods;
  • WEB-spline;
  • inf-sup condition;
  • diffusion equation;
  • navier–stokes equations

Abstract

In this article, we give some numerical techniques and error estimates using web-spline based mesh-free finite element method for the heat equation and the time-dependent Navier–Stokes equations on bounded domains. The web-spline method uses weighted extended B-splines on a regular grid as basis functions and does not require any grid generation. We demonstrate the method by providing numerical results for the Poisson's and stationary Stokes equation. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013