hp-FEM for three-dimensional elastic plates
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) no. 4, p. 597-630
In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in the energy norm for the degree p=𝒪(logε) and with 𝒪(p 4 ) degrees of freedom.
@article{M2AN_2002__36_4_597_0,
     author = {Dauge, Monique and Schwab, Christoph},
     title = {$hp$-FEM for three-dimensional elastic plates},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     pages = {597-630},
     doi = {10.1051/m2an:2002027},
     zbl = {1070.74046},
     mrnumber = {1932306},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_4_597_0}
}
Dauge, Monique; Schwab, Christoph. $hp$-FEM for three-dimensional elastic plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) no. 4, pp. 597-630. doi : 10.1051/m2an:2002027. http://www.numdam.org/item/M2AN_2002__36_4_597_0/

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