Abstract
AbstractIn this work, we apply the hypercircle method to Discontinuous Galerkin (DG) approximations of second order diffusion problems featuring inhomogeneous Dirichlet and Neumann boundary conditions. We focus on the interior penalty discontinuous Galerkin (IPDG) approximations of diffusion problems in primal variational formulation and produce a Prager–Synge theorem for such DG methods. Using the hypercircle method, we derive an a posteriori error estimator in terms of an equilibrated flux. The estimator is proven to be reliable and efficient. Numerical results are presented which illustrate the estimator’s performance.
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. Ainsworth, M.: A posteriori error estimation for discontinuous Galerkin finite element approximation. SIAM J. Numer. Anal. 45(4), 1777–1798 (2007)
2. Ainsworth, M.; Oden, J.T.: A Posteriori Error Estimation in Finite Element Analysis. Wiley, New York (2000)
3. Alnæs, M.S.; Blechta, J.; Hake, J.; Johansson, A.; Kehlet, B.; Logg, A.; Richardson, C.; Ring, J.; Rognes, M.E.; Wells, G.N.: The fenics project version 1.5. Arch. Numer. Softw. 3(100),9–13 (2015)
4. Arnold, D.N.; Brezzi, F.; Cockburn, B.; Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)
5. Bonito, A.; Nochetto, R.H.: Quasi-optimal convergence rate of an adaptive discontinuous Galerkin method. SIAM J. Numer. Anal. 48(2), 734–771 (2010)
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