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Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes
Author(s) -
Ainsworth Mark,
Rankin Richard
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20663
Subject(s) - mathematics , discontinuous galerkin method , finite element method , polygon mesh , upper and lower bounds , penalty method , galerkin method , element (criminal law) , order (exchange) , degree of a polynomial , polynomial , partial differential equation , mathematical analysis , mathematical optimization , geometry , physics , finance , economics , thermodynamics , political science , law
We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011