We present several a posteriori error estimators for the so-called hybridizable discontinuous
Galerkin (HDG) methods, as well as an a posteriori error estimator for variabledegree,
hybridized version of the Raviart-Thomas method on nonconforming meshes,
for second-order elliptic equations. We show that the error estimators provide a reliable
upper and lower bound for the true error of the flux in the L2-norm.
Moreover, we establish the convergence and quasi-optimality of adaptive hybridizable
discontinuous Galerkin (AHDG) methods. We prove that the so-called quasi-error,
that is, the sum of an energy-like error and a suitably scaled error estimator, is a contraction
between two consecutive loops. We also show that the AHDG methods achieve
optimal rates of convergence.
University of Minnesota Ph.D. dissertation. August 2012. Major: Mathematics. Advisor: Professor Bernardo Cockburn. 1 computer file (PDF); viii, 122 pages.
Convergence of adaptive hybridizable discontinuous Galerkin methods for second-order elliptic equations..
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