Stable Evaluation of Jacobian Matrices on Highly Refined Finite Element Meshes |
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Authors: | Email author" target="_blank">Arnd?MeyerEmail author |
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Affiliation: | (1) Department of Mathematics, TU Chemnitz, 09107 Chemnitz, Germany |
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Abstract: | In the adaptive finite element method, the solution of a p.d.e. is approximated by finer and finer meshes, which are controlled from error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. To overcome this problem we demonstrate a simple mechanism for red subdivision of triangles (and hanging nodes) and a more sophisticated technique for general quadrilaterals. |
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Keywords: | 65F10 65N30 65N22 |
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