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Discontinuous Galerkin derivative operators with applications to second‐order elliptic problems and stability
Author(s) -
Feng W.,
Lewis T. L.,
Wise S. M.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3440
Subject(s) - discontinuous galerkin method , mathematics , galerkin method , boundary value problem , finite element method , norm (philosophy) , dual (grammatical number) , penalty method , stability (learning theory) , mathematical analysis , mathematical optimization , computer science , art , physics , literature , machine learning , political science , law , thermodynamics
A discontinuous Galerkin (DG) finite‐element interior calculus is used as a common framework to describe various DG approximation methods for second‐order elliptic problems. Using the framework, symmetric interior‐penalty methods, local discontinuous Galerkin methods, and dual‐wind discontinuous Galerkin methods will be compared by expressing all of the methods in primal form. The penalty‐free nature of the dual‐wind discontinuous Galerkin method will be both motivated and used to better understand the analytic properties of the various DG methods. Consideration will be given to Neumann boundary conditions with numerical experiments that support the theoretical results. Many norm equivalencies will be derived laying the foundation for applying dual‐winding techniques to other problems. Copyright © 2015 John Wiley & Sons, Ltd.