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

Abstract

We study discontinuous Galerkin approximations of the $p$--biharmonic equation from a variational perspective. We propose a discrete variational formulation of the problem based on a appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a weak lower semicontinuity argument. We present numerical experiments aimed at testing the robustness of the method. We also note a superconvergence effect for some values of $p$.

22 pages, 3 figures

References in corpus (3)

• DOLFIN: Automated Finite Element Computing
• Discontinuous Galerkin methods for nonvariational problems
• Noether type discrete conserved quantities arising from a finite element approximation of a variational problem

Cited by in corpus (6)

• Discontinuous Galerkin Approach to Large Bending Deformation of a Bilayer Plate with Isometry Constraint
• Babuška-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshes
• An a posteriori analysis of some inconsistent, nonconforming Galerkin methods approximating elliptic problems
• Numerical analysis of the LDG method for large deformations of prestrained plates
• Discontinuous Galerkin methods for nonvariational problems
• LDG approximation of large deformations of prestrained plates