hp-version interior penalty DGFEMs for the biharmonic equation

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

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 ≥ 2. For a shape-regular family of meshes ? Partially supported by CNPq Brazil ?? Grant from CNPq Brazil Correspondence to: Endre Süli 2 Igor Mozolevski et al. co...

A PRIORI ERROR ANALYSIS FOR THE hp-VERSION OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE BIHARMONIC EQUATION

We consider the hp-version of the discontinuous Galerkin finite element approximation of boundary value problems for the biharmonic equation. Our main concern is the a priori error analysis of the method, based on a nonsymmetric bilinear form with interior discontinuity penalization terms. We establish an a priori error bound for the method which is of optimal order with respect to the mesh siz...

Numerical Analysis and Scientific Computing Preprint Seria A two-energies principle for the biharmonic equation and an a posteriori error estimator for an interior penalty discontinuous Galerkin approximation

Optimal Error Estimates for the hp–Version Interior Penalty Discontinuous Galerkin Finite Element Method

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for second-order linear reaction-diffusion equations. To the best of our knowledge, the sharpest known error bounds for the hp-DGFEM are due to Riviére, Wheeler and Girault [8] and due to Houston, Schwab and Süli [5] which are optimal with respect to the meshsize h but suboptimal with respect to ...

hp-Discontinuous Galerkin methods for the Helmholtz equation with large wave number

This paper develops some interior penalty hp-discontinuous Galerkin (hp-DG) methods for the Helmholtz equation in two and three dimensions. The proposed hp-DG methods are defined using a sesquilinear form which is not only mesh-dependent but also degree-dependent. In addition, the sesquilinear form contains penalty terms which not only penalize the jumps of the function values across the elemen...