Abstract
An adaptive finite element algorithm for elliptic boundary value problems in ℝ3 is presented. The algorithm uses linear finite elements, a-posteriori error estimators, a mesh refinement scheme based on bisection of tetrahedra, and a multi-grid solver. We show that the repeated bisection of an arbitrary tetrahedron leads to only a finite number of dissimilar tetrahedra, and that the recursive algorithm ensuring conformity of the meshes produced terminates in a finite number of steps. A procedure for assigning numbers to tetrahedra in a mesh based on a-posteriori error estimates, indicating the degree of refinement of the tetrahedron, is also presented. Numerical examples illustrating the effectiveness of the algorithm are given.
The work of the first auther as supported in part by NSF grants DMS-9500672 and DMS-9870399.
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Arnold, D.N., Mukherjee, A. (1999). Tetrahedral Bisection and Adaptive Finite Elements. In: Bern, M.W., Flaherty, J.E., Luskin, M. (eds) Grid Generation and Adaptive Algorithms. The IMA Volumes in Mathematics and its Applications, vol 113. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1556-1_2
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DOI: https://doi.org/10.1007/978-1-4612-1556-1_2
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