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A deluxe FETI‐DP algorithm for a hybrid staggered discontinuous Galerkin method for H(curl)‐elliptic problems
Author(s) -
Chung Eric T.,
Kim Hyea Hyun
Publication year - 2014
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.4617
Subject(s) - finite element method , lagrange multiplier , mathematics , basis function , feti , discontinuous galerkin method , curl (programming language) , convergence (economics) , mathematical analysis , algorithm , domain decomposition methods , mathematical optimization , computer science , engineering , structural engineering , economics , programming language , economic growth
SUMMARY Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound of C (1 + log( H ∕ h )) 2 , independent of the two parameters, where H ∕ h is the number of triangles across each subdomain. Numerical results are included to confirm our theoretical bounds. Copyright © 2013 John Wiley & Sons, Ltd.