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

Bernardo Cockburn, Weifeng Qiu, Manuel Solano

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24 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)665-699
Number of pages35
JournalMathematics of Computation
Volume83
Issue number286
DOIs
StatePublished - Jan 13 2014

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