Discontinuous Galerkin methods for the biharmonic problem

E. H. Georgoulis, P. Houston
2008 IMA Journal of Numerical Analysis  
Access from the University of Nottingham repository: Abstract This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini ([1]; SIAM J. Numer. Anal. 39, 5 (2001/02), 1749-1779) developed for the Poisson problem, to the design of DG methods via an appropriate choice of numerical flux functions for
more » ... ourth order problems; as an example we retrieve the interior penalty DG method developed by Süli & Mozolevski ([22]; Comput. Methods Appl. Mech. Engrg. 196, 13-16 (2007) , 1851-1863). The second part of this work is concerned with a new a-priori error analysis of the hp-version interior penalty DG method, when the error is measured in terms of both the energy-norm and L 2 -norm, as well certain linear functionals of the solution, for elemental polynomial degrees p ≥ 2. Also, provided that the solution is piecewise analytic in an open neighbourhood of each element, exponential convergence is also proven for the p-version of the DG method. The sharpness of the theoretical developments is illustrated by numerical experiments.
doi:10.1093/imanum/drn015 fatcat:ggntq5soanauphqiu3mgmqu2qq