Paper Info
Title
hp-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains.
Abstract
In this paper we introduce the hp-version discontinuous Galerkin composite finite element method for the discretization of second-order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or microstructures. While standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the minimal dimension of the underlying composite finite element space is independent of the number of geometric features. The key idea in the construction of this latter class of methods is that the computational domain Omega is no longer resolved by the mesh; instead, the finite element basis (or shape) functions are adapted to the geometric details present in Omega. In this paper, we extend these ideas to the discontinuous Galerkin setting, based on employing the hp-version of the finite element method. Numerical experiments highlighting the practical application of the proposed numerical scheme will be presented.
Year
DOI
Venue
2013
10.1137/120877246
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
composite finite element methods,discontinuous Galerkin methods,hp-version finite element methods
Discontinuous Galerkin method,Discretization,Mathematical optimization,Mathematical analysis,Composite number,Extended finite element method,Finite element method,Numerical analysis,Elliptic partial differential equation,Mathematics,Mixed finite element method
Journal
Volume
Issue
ISSN
35
3
1064-8275
Citations 
PageRank 
References 
16
0.93
3
Authors
3
Name
Order
Citations
PageRank
Paola F. Antonietti110414.21
Stefano Giani2369.55
Paul Houston317215.86