Geodesic
hp-FEM for three-dimensional elastic plates
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 597-630

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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.

DOI : 10.1051/m2an:2002027
Classification : 65N30, 74K20
Keywords: plates, hp-finite elements, exponential convergence, asymptotic expansion 
@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 },
     pages = {597--630},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/m2an:2002027},
     mrnumber = {1932306},
     zbl = {1070.74046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002027/}
}
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Dauge, Monique; Schwab, Christoph. $hp$-FEM for three-dimensional elastic plates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 597-630. doi: 10.1051/m2an:2002027

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