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Effect of numerical integration on meshless methods |
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| Authors: | Ivo Babu&#x;ka Uday Banerjee John E Osborn Qinghui Zhang |
| Affiliation: | aInstitute for Computational Engineering and Sciences, ACE 6.412, University of Texas at Austin, Austin, TX 78712, United States;bDepartment of Mathematics, 215 Carnegie, Syracuse University, Syracuse, NY 13244, United States;cDepartment of Mathematics, University of Maryland, College Park, MD 20742, United States;dDepartment of Scientific Computing and Computer Applications, Sun Yat-Sen University, Guangzhou 510275, PR China |
| Abstract: | In this paper, we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k 1. The meshless method was used on a second order Neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration. This estimate was obtained under the assumption that the numerical integration scheme satisfied a form of Green’s formula. We also indicated how to obtain numerical integration schemes satisfying this property. |
| Keywords: | Galerkin methods Meshless methods Quadrature Numerical integration Error estimates |
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