$hp$-FEM for three-dimensional elastic plates

Dauge, Monique; Schwab, Christoph

doi:10.1051/m2an:2002027

Geodesic

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h p

-FEM for three-dimensional elastic plates

Dauge, Monique ; Schwab, Christoph

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 4, pp. 597-630

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Résumé

In this work, we analyze hierarchic $h p$ -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 $h p$ -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 $h p$ -discretization is consistent with the three-dimensional solution to any power of $ε$ in the energy norm for the degree $p = 𝒪 (|log ε|)$ and with $𝒪 (p^{4})$ degrees of freedom.

MR Zbl

DOI : 10.1051/m2an:2002027

Classification : 65N30, 74K20
Keywords: plates, hp-finite elements, exponential convergence, asymptotic expansion

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     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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