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Authors:
Houman Borouchaki
Patrick Laug
Keywords: a posteriori error estimation; interpolation error; mesh adaptation; surface curvature.
Abstract:
An essential prerequisite for the numerical finite element simulation of physical problems expressed in terms of PDEs is the construction of an adequate mesh of the domain. This first stage, which usually involves a fully automatic mesh generation method, is then followed by a computational step. One can show that the quality of the solution strongly depends on the shape quality of the mesh of the domain. At the second stage, the numerical solution obtained with the initial mesh is generally analyzed using an appropriate a posteriori error estimator which, based on the quality of the solution, indicates whether or not the solution is accurate. The quality of the solution is closely related to how well the mesh corresponds to the underlying physical phenomenon, which can be quantified by the element sizes of the mesh. An a posteriori error estimation based on the interpolation error depending on the Hessian of the solution seems to be well adapted to the purpose of adaptive meshing. In this paper, we propose a new interpolation error estimation based on the local deformation of the Cartesian surface representing the solution. This methodology is generally used in the context of surface meshing. In our example, the proposed methodology is applied to minimize the interpolation error on an image whose grey level is considered as being the solution.
Pages: 81 to 86
Copyright: Copyright (c) IARIA, 2010
Publication date: October 25, 2010
Published in: conference
ISSN: 2308-4499
ISBN: 978-1-61208-101-4
Location: Florence, Italy
Dates: from October 25, 2010 to October 30, 2010