All Outputs (74)

Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes (2017)
Journal Article
Antonietti, P. F., Houston, P., Hu, X., Sarti, M., & Verani, M. (in press). Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Numerische Mathematik, 54(4), https://doi.org/10.1007/s10092-017-0223-6

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of s... Read More about Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes.

Adjoint error estimation and adaptivity for hyperbolic problems (2017)
Book Chapter
Houston, P. (2017). Adjoint error estimation and adaptivity for hyperbolic problems. In R. Abgrall, & C. Shu (Eds.), Handbook of Numerical Methods for Hyperbolic Problems. Applied and Modern Issues. Elsevier / North Holland

In this article we present an overview of a posteriori error estimation and adaptive mesh design for hyperbolic/nearly-hyperbolic problems. In particular, we discuss the question of error estimation for general target functionals of the solution; typ... Read More about Adjoint error estimation and adaptivity for hyperbolic problems.

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains (2016)
Book Chapter
Antonietti, P. F., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E. H., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. R. Barrenechea, F. Brezzi, A. Cangiani, & E. H. Georgoulis (Eds.), Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations (281-310). Cham: Springer Publishing Company. https://doi.org/10.1007/978-3-319-41640-3_9

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of st... Read More about Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains.

Adaptive discontinuous Galerkin methods on polytopic meshes (2016)
Conference Proceeding
Collis, J., & Houston, P. (2016). Adaptive discontinuous Galerkin methods on polytopic meshes.

In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on c... Read More about Adaptive discontinuous Galerkin methods on polytopic meshes.

hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes (2016)
Journal Article
Cangiani, A., Dong, Z., Georgoulis, E. H., & Houston, P. (2016). hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis, 50(3), 699-725. https://doi.org/10.1051/m2an/2015059

We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopi... Read More about hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes.

Adaptive energy minimisation for hp-finite element methods (2016)
Journal Article
Houston, P., & Wihler, T. P. (2016). Adaptive energy minimisation for hp-finite element methods. Computers and Mathematics with Applications, 71(4), https://doi.org/10.1016/j.camwa.2016.01.002

This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adapti... Read More about Adaptive energy minimisation for hp-finite element methods.

Flows of granular material in two-dimensional channels (2015)
Journal Article
Bain, O., Billingham, J., Houston, P., & Lowndes, I. (2015). Flows of granular material in two-dimensional channels. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-015-9810-1

Secondary cone-type crushing machines are an important part of the aggregate production process. These devices process roughly crushed material into aggregate of greater consistency and homogeneity. We apply a continuum model for granular materials (... Read More about Flows of granular material in two-dimensional channels.

A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods (2015)
Journal Article
Antonietti, P. F., Houston, P., & Smears, I. A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods. Manuscript submitted for publication

In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial dif... Read More about A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods.

Goal-oriented a posteriori error estimation for the travel time functional in porous media flows (2015)
Journal Article
Cliffe, A., Collis, J., & Houston, P. (2015). Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. SIAM Journal on Scientific Computing, 37(2), Article B127-B152. https://doi.org/10.1137/140960499

In this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows. The key application of this work is in the safety assessment of ra... Read More about Goal-oriented a posteriori error estimation for the travel time functional in porous media flows.

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.

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?.

Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows (2013)
Conference Proceeding
Cliffe, A., Hall, E., & Houston, P. (2013). Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows.

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.

Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration (2013)
Conference Proceeding
Congreve, S., & Houston, P. (2013). Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration.

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.