hp -Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation. - Mozolevski, I; Süli, E; Bösing, P (2007)
We consider the symmetric formulation of the interior penalty discontinuous Galerkin finite element method for the numerical solution of the biharmonic equation with Dirichlet boundary conditions in a bounded polyhedral domain in ℝ d, d ≥ 2. For a shape-regular family of meshes consisting of parallelepipeds, we derive hp-version a priori bounds on the global error measured in the L 2 norm and in broken Sobolev norms. Using these, we obtain hp-version bounds on the error in linear functionals of the solution. The bounds are optimal with respect to the mesh size h and suboptimal with respect to the degree of the piecewise polynomial approximation p. The theoretical results are confirmed by numerical experiments, and some practical applications in Poisson-Kirchhoff thin plate theory are presented. © Springer Science+Business Media, LLC 2007.