Adaptive n-Sided Polygonal Finite Element Method for Analysis of Plane Problems

Balaji, K S and Amirtham, Rajagopal (2013) Adaptive n-Sided Polygonal Finite Element Method for Analysis of Plane Problems. Masters thesis, Indian Institute of Technology, Hyderabad.

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Abstract

In this work we present an adaptive polygonal nite element method for analysis of two dimensional plane problems. The generation of n sided polygonal nite element mesh is based on generation of a centroidal Vorononi tessellation (CVT). By this method an unstructured tessellation of a scattered point set, that minimally covers the proximal space around each point in the point set can be generated. The method has also been extended to include tessellation for non convex domains. For the numerical integration of Galerkin weak form over polygonal nite element domains we resort to classical Gaussian quadrature applied on triangular sub domains of each polygonal element. An adaptive nite element analysis strategy is proposed and implemented in the present work. A patch recovery type of stress smoothing technique that utilizes polygonal element patches for obtaining smooth stresses has been proposed for obtaining the smoothed nite element stresses. A classical z2 type a - posteriori error estimator that estimates the energy norm of the error from the recovered solution is then implemented. The renement of the polygonal elements is made on an element by element basis through a renement index. Numerical examples of two dimensional plane problems are presented to demonstrate the eciency of the proposed adaptive polygonal nite element method.

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