Journal of Scientific Computing

, Volume 30, Issue 3, pp 465–491 | Cite as

hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation

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Abstract

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 \(\mathbb{R}^d, d \geqslant 2\). For a shape-regular family of meshes consisting of parallelepipeds, we derive hp-version a priori bounds on the global error measured in the L2 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.

Keywords

High-order elliptic equations finite element methods discontinuous Galerkin methods a priori error analysis linear functionals 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Igor Mozolevski
    • 1
  • Endre Süli
    • 2
  • Paulo R. Bösing
    • 3
  1. 1.Mathematics DepartmentFederal University of Santa CatarinaTrindadeBrazil
  2. 2.Computing LaboratoryUniversity of OxfordOxfordUK
  3. 3.Applied Mathematics Department, IMEUniversity of São PauloSão PauloBrazil

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