Paper Info
Title
Two-Grid hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic PDEs.
Abstract
In this article we propose a class of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of monotone type. The key idea in this setting is to first discretise the underlying nonlinear problem on a coarse finite element space \(V({{\mathcal {T}_{H}}},\boldsymbol {P})\). The resulting ‘coarse’ numerical solution is then exploited to provide the necessary data needed to linearise the underlying discretisation on the finer space \(V({{\mathcal {T}_{h}}},\boldsymbol {p})\); thereby, only a linear system of equations is solved on the richer space \(V({{\mathcal {T}_{h}}},\boldsymbol {p})\). In this article both the a priori and a posteriori error analysis of the two-grid hp-version discontinuous Galerkin finite element method is developed. Moreover, we propose and implement an hp-adaptive two-grid algorithm, which is capable of designing both the coarse and fine finite element spaces \(V({{\mathcal {T}_{H}}},\boldsymbol {P})\) and \(V({{\mathcal {T}_{h}}},\boldsymbol {p})\), respectively, in an automatic fashion. Numerical experiments are presented for both two- and three-dimensional problems; in each case, we demonstrate that the CPU time required to compute the numerical solution to a given accuracy is typically less when the two-grid approach is exploited, when compared to the standard discontinuous Galerkin method.
Year
DOI
Venue
2013
10.1007/s10915-012-9644-1
J. Sci. Comput.
Keywords
Field
DocType
hp-finite element methods, Discontinuous Galerkin methods, Adaptivity, Two-grid methods, Quasilinear PDEs
Discontinuous Galerkin method,Discretization,Mathematical optimization,Nonlinear system,System of linear equations,Mathematical analysis,Finite element method,Mathematics,Grid,Monotone polygon,Elliptic boundary value problem
Journal
Volume
Issue
ISSN
55
2
1573-7691
Citations 
PageRank 
References 
2
0.43
13
Authors
3
Name
Order
Citations
PageRank
Scott Congreve131.46
Paul Houston28922.34
Thomas P. Wihler310414.67