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
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},
     year = {2014},
     volume = {41},
     zbl = {1302.65257},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a8/}
}
TY  - JOUR
AU  - Pryer,  Tristan
TI  - Discontinuous Galerkin methods for the \(p\)-biharmonic equation from a discrete variational perspective
JO  - Electronic transactions on numerical analysis
PY  - 2014
SP  - 328
EP  - 349
VL  - 41
UR  - http://geodesic.mathdoc.fr/item/ETNA_2014__41__a8/
LA  - en
ID  - ETNA_2014__41__a8
ER  - 
%0 Journal Article
%A Pryer,  Tristan
%T Discontinuous Galerkin methods for the \(p\)-biharmonic equation from a discrete variational perspective
%J Electronic transactions on numerical analysis
%D 2014
%P 328-349
%V 41
%U http://geodesic.mathdoc.fr/item/ETNA_2014__41__a8/
%G en
%F ETNA_2014__41__a8
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/