A Petrov-Galerkin Natural Element Method Securing the Numerical Integration Accuracy
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An improved meshfree method called the Petrov-Galerkin natural element (PG-NE) method is introduced in order to secure the numerical integration accuracy. As in the Bubnov-Galerkin natural element (BG-NE) method, we use Laplace interpolation function for the trial basis function and Delaunay triangles to define a regular integration background mesh. But, unlike the BG-NE method, the test basis function is differently chosen, based on the Petrov-Galerkin concept, such that its support coincides exactly with a regular integration region in background mesh. Illustrative numerical experiments verify that the present method successfully prevents the numerical accuracy deterioration stemming from the numerical integration error.
Key WordsPetrov-Galerkin Natural Element Method Laplace Interpolation Function Constant Strain Basis Function Numerical Integration Accuracy Convergence Assessment
- ANSYS, Inc., 1998, User’s Manual (ver. 5.5.1), Houston, PA.Google Scholar
- Piper, P., 1993, “Properties of Local Coordinates based on Dirichlet Tessellations,”in Farin, G, Hagan, H. and Noltemeier, H. (eds.),Geometric Modelling, Vol. 8, pp. 227–239.Google Scholar
- Traversoni, L., 1994, “Natural Neighbor Finite Elements,”Proc. Int. Conf. Hydraulic Engineering Software, Vol. 2, pp. 291–297.Google Scholar
- Zienkiewicz, O. C. and Taylor, R. L., 1989,The Finite Element Method: Basic Formulation and Linear Problems, McGraw-Hill, Singapore.Google Scholar