WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 9, 2014
An Efficient Error Indicator with Mesh Smoothing for Mesh Refinement: Application to Poisson and Laplace Problems
Authors: , ,
Abstract: An efficient mesh refinement method for h-version finite element analysis is presented based on both an a-posteriori error indicator and the geometrical quality of mesh. The first step is to refine the meshes on which the a-posteriori error indicators are relatively higher than the others. The error indicators are obtained by simplifying the computation of error bounds which are obtained by solving elemental Neumann type subproblems with the averaged flux for the consistency of the Neumann problems. The simplification of computation means that the functional space on the mesh uniformly refined with only half size of the coarse mesh is chosen as the test functional space in the elemental residual form of error equations, thus the cost for computing the error indicators is quite low. After refinement, some refined triangles will become poorly shaped or distorted, then the second step is to move the meshes to improve their geometrical quality with Laplacian smoothing algorithm. Two examples are computed to verify this method and the results show that the refined mesh obtained by both the a-posteriori error indicator and mesh smoothing gives the optimal convergence and higher accuracy for the results.
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Pages: 206-214
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 9, 2014, Art. #18