Outputs (74)

hp-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains (2014)
Journal Article
Giani, S., & Houston, P. (2014). hp-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30(4), https://doi.org/10.1002/num.21872

In this paper we develop the a posteriori error estimation of hp-version discontinuous Galerkin composite finite element methods for the discretization of second order elliptic partial differential equations. This class of methods allows for the appr... Read More about hp-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains.

Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains (2014)
Journal Article
Antonietti, P. F., Giani, S., & Houston, P. (2014). Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Journal of Scientific Computing, 60(1), https://doi.org/10.1007/s10915-013-9792-y

In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized... Read More about Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains.

Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows (2014)
Journal Article
Giani, S., & Houston, P. (2014). Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows. Numerical Mathematics, 7(2), https://doi.org/10.1017/S100489790000091X

In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, w... Read More about Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows.

hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes (2014)
Journal Article
Cangiani, A., Georgoulis, E. H., & Houston, P. (2014). hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 24(10), 2009-2041. https://doi.org/10.1142/S0218202514500146

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analy... Read More about hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes.

Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows (2014)
Journal Article
Congreve, S., & Houston, P. (2014). Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. International Journal of Numerical Analysis and Modeling, 11(3),

In this article we consider the a priori and a posteriori error analysis of two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a strongly monotone quasi-Newtonian fluid flow problem. The basis of the two-g... Read More about Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows.

hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows (2013)
Journal Article
Cliffe, A., Hall, E., & Houston, P. (2014). hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Computers and Mathematics with Applications, 67(4), https://doi.org/10.1016/j.camwa.2013.09.024

In this article we consider the a posteriori error estimation and adaptive mesh refinement of hp-version discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations... Read More about hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows.

hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains (2013)
Journal Article
Antonietti, P. F., Giani, S., & Houston, P. (2013). hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM Journal on Scientific Computing, 35(3), Article A1417-A1439. https://doi.org/10.1137/120877246

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 c... Read More about hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains.

Is a persistent global bias necessary for the establishment of planar cell polarity? (2013)
Journal Article
Fischer, S., Houston, P., Monk, N. A., & Owen, M. R. (2013). Is a persistent global bias necessary for the establishment of planar cell polarity?. PLoS ONE, 8(4), 1-12. https://doi.org/10.1371/journal.pone.0060064

Planar cell polarity (PCP) — the coordinated polarisation of a whole field of cells within the plane of a tissue — relies on the interaction of three modules: a global module that couples individual cellular polarity to the tissue axis, a local modul... Read More about Is a persistent global bias necessary for the establishment of planar cell polarity?.

Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration (2013)
Presentation / Conference Contribution
Congreve, S., & Houston, P. Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration. Presented at Proceedings of the Eighth International Conference on Scientific Computing and Applications

In this paper 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 based on the application of a single step of a no... Read More about Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration.

Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows (2013)
Presentation / Conference Contribution
Cliffe, A., Hall, E., & Houston, P. Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. Presented at Numerical Mathematics and Advanced Applications, ENUMATH 2011

In this article we consider the a posteriori error estimation and adaptive mesh refinement of hp-version discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations... Read More about Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows.