Volume 41, pp. 328-349, 2014.

Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

Tristan Pryer

Abstract

We study discontinuous Galerkin approximations of the $p$-biharmonic equation for $p\in (1,\mathrm{\infty })$ 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.

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Key words

discontinuous Galerkin finite element method, discrete variational problem, $p$-biharmonic equation

AMS subject classifications

65N30, 65K10, 35J40