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Title: A high-order hybridizable discontinuous Galerkin method for elliptic interface problems
Authors: Huynh, L.N.T.
Nguyen, N.C.
Peraire, J.
Khoo, B.C. 
Keywords: Curvilinear interface
Discontinuous Galerkin
Elliptic partial differential equation
Jump condition
Mixed/hybrid method
Superparametric element
Issue Date: 13-Jan-2013
Citation: Huynh, L.N.T., Nguyen, N.C., Peraire, J., Khoo, B.C. (2013-01-13). A high-order hybridizable discontinuous Galerkin method for elliptic interface problems. International Journal for Numerical Methods in Engineering 93 (2) : 183-200. ScholarBank@NUS Repository.
Abstract: We present a high-order hybridizable discontinuous Galerkin method for solving elliptic interface problems in which the solution and gradient are nonsmooth because of jump conditions across the interface. The hybridizable discontinuous Galerkin method is endowed with several distinct characteristics. First, they reduce the globally coupled unknowns to the approximate trace of the solution on element boundaries, thereby leading to a significant reduction in the global degrees of freedom. Second, they provide, for elliptic problems with polygonal interfaces, approximations of all the variables that converge with the optimal order of k+1 in the L2(Ω)-norm where k denotes the polynomial order of the approximation spaces. Third, they possess some superconvergence properties that allow the use of an inexpensive element-by-element postprocessing to compute a new approximate solution that converges with order k+2. However, for elliptic problems with finite jumps in the solution across the curvilinear interface, the approximate solution and gradient do not converge optimally if the elements at the interface are isoparametric. The discrepancy between the exact geometry and the approximate triangulation near the curved interfaces results in lower order convergence. To recover the optimal convergence for the approximate solution and gradient, we propose to use superparametric elements at the interface. © 2012 John Wiley & Sons, Ltd.
Source Title: International Journal for Numerical Methods in Engineering
ISSN: 00295981
DOI: 10.1002/nme.4382
Appears in Collections:Staff Publications

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