Professor PAUL HOUSTON's Outputs (6)

Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows (2014)
Journal Article
Giani, S., & Houston, P. (2014). Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270, https://doi.org/10.1016/j.cam.2014.03.007

In this article we consider the application of goal-oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the di... Read More about Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows.

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.