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Algebraic multilevel iteration method for lowest order Raviart–Thomas space and applications
Author(s) -
Kraus J. K.,
Tomar S. K.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3103
Subject(s) - discretization , mathematics , finite element method , discontinuous galerkin method , algebraic equation , boundary value problem , galerkin method , algebraic number , a priori and a posteriori , space (punctuation) , iterative method , mathematical analysis , mathematical optimization , nonlinear system , computer science , operating system , philosophy , physics , epistemology , quantum mechanics , thermodynamics
An optimal order algebraic multilevel iterative method for solving system of linear algebraic equations arising from the finite element discretization of certain boundary value problems, that have their weak formulation in the space H ( div ), is presented. The algorithm is developed for the discrete problem obtained by using the lowest‐order Raviart–Thomas space. The method is theoretically analyzed and supporting numerical examples are presented. Furthermore, as a particular application, the algorithm is used for the solution of the discrete minimization problem which arises in the functional‐type a posteriori error estimates for the discontinuous Galerkin approximation of elliptic problems. Copyright © 2011 John Wiley & Sons, Ltd.