Geodesic
Discontinuous Galerkin methods for the $p$-biharmonic equation from a discrete variational perspective
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 328-349.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study discontinuous Galerkin approximations of the $p$-biharmonic equation for $p\in (1,\infty)$ from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.
Classification : 65N30, 65K10, 35J40
Keywords: discontinuous Galerkin finite element method, discrete variational problem, $p$-biharmonic equation 
@article{ETNA_2014__41__a8,
     author = {Pryer, Tristan},
     title = {Discontinuous {Galerkin} methods for the $p$-biharmonic equation from a discrete variational perspective},
     journal = {Electronic transactions on numerical analysis},
     pages = {328--349},
     publisher = {mathdoc},
     volume = {41},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a8/}
}
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Pryer, Tristan. Discontinuous Galerkin methods for the $p$-biharmonic equation from a discrete variational perspective. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 328-349. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a8/