@Article{IJNAM-3-1,
author = {Peter, Moore, K.},
title = {Effects of Basis Selection and H-Refinement on Error Estimator Reliability and Solution Efficiency for High-Order Methods in Three Space Dimensions},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2006},
volume = {3},
number = {1},
pages = {21--51},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2006-IJNAM-888},
url = {https://global-sci.com/article/83812/effects-of-basis-selection-and-h-refinement-on-error-estimator-reliability-and-solution-efficiency-for-high-order-methods-in-three-space-dimensions}
}