Effects of Basis Selection and H-Refinement on Error Estimator Reliability and Solution Efficiency for High-Order Methods in Three Space Dimensions
Year: 2006
Author: Peter K. Moore
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 1 : pp. 21–51
Abstract
Designing effective high-order adaptive methods for solving stationary reaction-diffusion equations in three dimensions requires the selection of a finite element basis, a posteriori error estimator and refinement strategy. Estimator accuracy may depend on the basis chosen, which in turn, may lead to unreliability or inefficiency via under- or over-refinement, respectively. The basis may also have an impact on the size and condition of the matrices that arise from discretization, and thus, on algorithm effectiveness. Herein, the interaction between these three components is studied in the context of an $h$-refinement procedure. The effects of these choices on the robustness and efficiency of the algorithm are examined for several linear and nonlinear problems. The results demonstrate that popular choices such as the tensor-product basis or the modified Szabό-Babuška basis have significant shortcomings but that promising alternatives exist.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-IJNAM-888
International Journal of Numerical Analysis and Modeling, Vol. 3 (2006), Iss. 1 : pp. 21–51
Published online: 2006-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: a posteriori error estimation adaptivity high-order finite element basis.