A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)665-699
Journal / PublicationMathematics of Computation
Issue number286
Online published18 Jul 2013
Publication statusPublished - Mar 2014


We present the first a priori error analysis of a technique that allows us to numerically solve steady-state diffusion problems defined on curved domains Ω by using finite element methods defined in polyhedral subdomains Dh ⊂ Ω. For a wide variety of hybridizable discontinuous Galerkin and mixed methods, we prove that the order of convergence in the L2-norm of the approximate flux and scalar unknowns is optimal as long as the distance between the boundary of the original domain Γ and that of the computational domain Γh is of order h. We also prove that the L2-norm of a projection of the error of the scalar variable superconverges with a full additional order when the distance between Γ and Γh is of order h5/4 but with only half an additional order when such a distance is of order h. Finally, we present numerical experiments confirming the theoretical results and showing that even when the distance between Γ and Γh is of order h, the above-mentioned projection of the error of the scalar variable can still superconverge with a full additional order. © 2013 American Mathematical Society.

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