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An augmented LDG method for linear diffusion problems
Author(s) -
Barrios Tomás P.,
Bustinza Rommel
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700360
Subject(s) - discontinuous galerkin method , mathematics , estimator , convergence (economics) , operator (biology) , galerkin method , diffusion , order (exchange) , a priori and a posteriori , scheme (mathematics) , boundary (topology) , elliptic operator , mathematical analysis , finite element method , physics , thermodynamics , repressor , epistemology , gene , transcription factor , economics , economic growth , biochemistry , statistics , chemistry , philosophy , finance
In this note we present a review of a stabilized discontinuous Galerkin method for elliptic problems in the plane with mixed boundary conditions. The stabilized scheme is obtained by adding suitable Galerkin least‐squares terms. The corresponding unique solvability and optimal rates of convergence, with respect to the h –version, are established by applying the wellknown Lax‐Milgram theorem, avoiding therefore the introduction of any lifting operator for the analysis. Furthermore, we include a reliable and efficient (up to high order terms) a posteriori error estimator. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)