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Explicit k-dependence for Pk finite elements in Wm,p error estimates: application to probabilistic laws for accuracy analysis

Abstract : We derive an explicit k-dependence in W m,p error estimates for P k Lagrange finite elements. Two laws of probability are established to measure the relative accuracy between P k 1 and P k 2 finite elements, (k 1 < k 2), in terms of W m,p-norms. We further prove a weak asymptotic relation in D (R) between these probabilistic laws when difference k 2 − k 1 goes to infinity. Moreover, as expected, one finds that P k 2 finite element is surely more accurate than P k 1 , for sufficiently small values of the mesh size h. Nevertheless, our results also highlight cases where P k 1 is more likely accurate than P k 2 , for a range of values of h. Hence, this approach brings a new perspective on how to compare two finite elements, which is not limited to the rate of convergence.
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https://hal-cnrs.archives-ouvertes.fr/hal-03837946
Contributor : joel chaska Connect in order to contact the contributor
Submitted on : Thursday, November 10, 2022 - 9:30:08 AM
Last modification on : Friday, November 11, 2022 - 4:02:56 AM

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Joël Chaskalovic, Franck Assous. Explicit k-dependence for Pk finite elements in Wm,p error estimates: application to probabilistic laws for accuracy analysis. Applicable Analysis, 2019, 100 (13), pp.2825-2843. ⟨10.1080/00036811.2019.1698727⟩. ⟨hal-03837946⟩

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