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Broglia, R., Choi, K.-S., Houston, Paul, Pasquale, L. and Zanchetta, Pericle (2018) Output feedback control of flow separation over an aerofoil using plasma actuators. International Journal of Numerical Analysis and Modeling, 15 (6). pp. 864-883. ISSN 1705-5105

Congreve, Scott, Houston, Paul and Perugia, Ilaria (2018) Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Advances in Computational Mathematics . ISSN 1572-9044 (In Press)

Houston, Paul and Sime, Nathan (2018) Automatic symbolic computation for discontinuous Galerkin finite element methods. SIAM Journal on Scientific Computing, 40 (3). C327-C357. ISSN 1064-8275

Houston, Paul and Wihler, Thomas P. (2018) An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of Computation . ISSN 1088-6842

Hall, Edward, Houston, Paul and Murphy, Steven (2017) hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems. SIAM Journal on Scientific Computing, 39 (5). B916-B942. ISSN 1095-7197

Houston, Paul and Wihler, Thomas P. (2017) An adaptive variable order quadrature strategy. Lecture Notes in Computational Science and Engineering, 119 . pp. 533-545. ISSN 1439-7358

Houston, Paul and Sime, Nathan (2017) Numerical modelling of MPA-CVD reactors with the discontinuous Galerkin finite element method. Journal of Physics D: Applied Physics, 50 (29). 295202/1-295202/16. ISSN 1361-6463

Cangiani, Andrea, Dong, Zhaonan, Georgoulis, Emmanuil H. and Houston, Paul (2016) hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (3). pp. 699-725. ISSN 0764-583X

Houston, Paul and Wihler, Thomas P. (2016) Adaptive energy minimisation for hp-finite element methods. Computers and Mathematics with Applications, 71 (4). pp. 977-990. ISSN 0898-1221

Bain, Oliver, Billingham, John, Houston, Paul and Lowndes, Ian (2015) Flows of granular material in two-dimensional channels. Journal of Engineering Mathematics . ISSN 0022-0833

Antonietti, Paola F., Houston, Paul and Smears, Iain (2015) A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling . ISSN 1705-5105 (Submitted)

Cliffe, Andrew, Collis, Joe and Houston, Paul (2015) Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. SIAM Journal on Scientific Computing, 37 (2). B127-B152. ISSN 1064-8275

Giani, Stefano and Houston, Paul (2014) Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270 . pp. 32-42. ISSN 0377-0427

Antonietti, Paola F., Giani, Stefano and Houston, Paul (2014) Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Journal of Scientific Computing, 60 (1). pp. 203-227. ISSN 0885-7474

Giani, Stefano and Houston, Paul (2014) hp-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30 (4). pp. 1342-1367. ISSN 0749-159X

Giani, Stefano and Houston, Paul (2014) Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows. Numerical Mathematics: Theory, Methods and Applications, 7 (2). pp. 123-128. ISSN 1004-8979

Cliffe, Andrew, Hall, Edward and Houston, Paul (2014) hp-Adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Computers and Mathematics with Applications, 67 (4). pp. 796-806. ISSN 0898-1221

Cangiani, Andrea, Georgoulis, Emmanuil H. and Houston, Paul (2014) hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 24 (10). pp. 2009-2041. ISSN 0218-2025

Congreve, Scott and Houston, Paul (2014) Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. International Journal of Numerical Analysis and Modeling, 11 (3). pp. 496-524. ISSN 1705-5105

Antonietti, Paola F., Giani, Stefano and Houston, Paul (2013) hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM Journal on Scientific Computing, 35 (3). A1417-A1439. ISSN 1064-8275

Fischer, Sabine, Houston, Paul, Monk, Nick A.M. and Owen, Markus R. (2013) Is a persistent global bias necessary for the establishment of planar cell polarity? PLoS ONE, 8 (4). e60064. ISSN 1932-6203

Cliffe, Andrew, Hall, Edward, Houston, Paul, Phipps, Eric T. and Salinger, Andrew G. (2012) Adaptivity and a posteriori error control for bifurcation problems III: incompressible fluid flow in open systems with O(2) symmetry. Journal of Scientific Computing, 52 (2). pp. 153-179. ISSN 0885-7474 (Submitted)

Congreve, Scott, Houston, Paul, Süli, Endre and Wihler, Thomas P. (2012) Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows. IMA Journal of Numerical Analysis . ISSN 0272-4979 (Submitted)

Giani, Stefano and Houston, Paul (2011) Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. International Journal of Numerical Analysis and Modeling . ISSN 1705-5105 (Submitted)

Houston, Paul and Wihler, Thomas P. (2011) Discontinuous Galerkin methods for problems with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis . ISSN 0764-583X (Submitted)

Congreve, Scott, Houston, Paul and Wihler, Thomas P. (2011) Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proceedings in Applied Mathematics and Mechanics, 11 (1). pp. 3-6. ISSN 1617-7061

Cliffe, Andrew, Hall, Edward, Houston, Paul, Phipps, Eric T. and Salinger, Andrew G. (2010) Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8 (4). pp. 845-865. ISSN 1815-2406 (Submitted)

Cliffe, Andrew, Hall, Edward, Houston, Paul, Phipps, Eric T. and Salinger, Andrew G. (2010) Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. Journal of Scientific Computing . ISSN 0885-7474 (Submitted)

Milne, Andrew, Cliffe, Andrew, Holton, David, Houston, Paul, Jackson, C. Peter and Joyce, Steve (2010) A new method for conditioning stochastic groundwater flow models in fractured media. Advances in Water Resources . ISSN 0309-1708 (Submitted)

Houston, Paul and Wihler, Thomas P. (2009) Second-order elliptic PDE with discontinuous boundary data. IMA Journal of Numerical Analysis . ISSN 0272-4979 (Submitted)

Antonietti, Paola F. and Houston, Paul (2009) A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods. Journal of Scientific Computing . ISSN 0885-7474 (Submitted)

Antonietti, Paola F. and Houston, Paul (2009) An hr-adaptive discontinuous Galerkin method for advection-diffusion problems. Communications to SIMAI Congress, 3 . ISSN 1827-9015 (Submitted)

Zhu, Liang, Giani, Stefano, Houston, Paul and Schoetzau, Dominik (2009) Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Mathematical Models and Methods in Applied Sciences (M3AS) . ISSN 0218-2025 (Submitted)

Houston, Paul, Schoetzau, Dominik and Wei, Xiaoxi (2008) A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics. Journal of Scientific Computing . (Submitted)

Cliffe, Andrew, Hall, Edward and Houston, Paul (2008) Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. SIAM Journal on Scientific Computing . ISSN 1064-8275 (Submitted)

Georgoulis, Emmanuil H., Houston, Paul and Virtanen, Juha (2008) An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems. IMA Journal of Numerical Analysis . (Submitted)

Schamberg, Sabine, Houston, Paul, Monk, Nick A.M. and Owen, Markus R. (2008) Modelling and analysis of planar cell polarity. Bulletin of Mathematical Biology . ISSN 0092-8240 (Submitted)

Houston, Paul, Suli, Endre and Wihler, Thomas P. (2006) A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems.

Georgoulis, Emmanuil H., Hall, Edward and Houston, Paul (2006) Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes.

Georgoulis, Emmanuil H., Hall, Edward and Houston, Paul (2006) Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis.

Hartmann, Ralf and Houston, Paul (2005) Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation.

Hartmann, Ralf and Houston, Paul (2005) Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation.

Houston, Paul, Perugia, Ilaria and Schoetzau, Dominik (2005) A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations.

Buffa, Annalisa, Houston, Paul and Perugia, Ilaria (2005) Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes.

Brownlee, R., Houston, Paul, Levesley, J. and Rosswog, S. (2005) Enhancing SPH using moving least-squares and radial basis functions.

Antonietti, Paola F. and Houston, Paul A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems. International Journal of Numerical Analysis and Modeling . (Submitted)

Hartmann, Ralf and Houston, Paul An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations. Journal of Computational Physics . ISSN 0021-9991 (Submitted)

Georgoulis, Emmanuil H. and Houston, Paul Discontinuous Galerkin Methods for the Biharmonic Problem. IMA Journal of Numerical Analysis . (Submitted)

Georgoulis, Emmanuil H., Hall, Edward and Houston, Paul Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity. Applied Numerical Mathematics . (Submitted)

Fischer, Sabine, Houston, Paul, Monk, Nick A.M. and Owen, Markus R. Is a persistent global bias necessary for the establishment of planar cell polarity? PLoS Computational Biology . ISSN 1553-734X (Submitted)

Congreve, Scott, Houston, Paul and Wihler, Thomas P. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Journal of Scientific Computing . ISSN 0885-7474 (Submitted)

Conference or Workshop Item

Collis, Joe and Houston, Paul (2016) Adaptive discontinuous Galerkin methods on polytopic meshes. In: X-DMS eXtended Discretization Methods, 9-11 Sept 2015, Ferrara, Italy.

Cliffe, Andrew, Hall, Edward and Houston, Paul (2013) Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. In: Numerical Mathematics and Advanced Applications, ENUMATH 2011, 5-9 September 2011, Leicester, UK.

Congreve, Scott and Houston, Paul (2013) Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration. In: Proceedings of the Eighth International Conference on Scientific Computing and Applications, 1-4 April 2012, Las Vegas, USA.

Congreve, Scott, Houston, Paul and Wihler, Thomas P. (2013) hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. In: Numerical Mathematics and Advanced Applications, ENUMATH 2011, 5-9 September 2011, Leicester, UK.

Antonietti, Paola F. and Houston, Paul (2011) Preconditioning high-order discontinuous Galerkin discretizations of elliptic problems. In: 20th International Conference on Domain Decomposition Methods, 7-11 Feb 2011, UC San Diego, California, USA. (Submitted)

Houston, Paul, Georgoulis, Emmanuil H. and Hall, Edward (2006) Adaptivity and A Posteriori Error Estimation For DG Methods on Anisotropic Meshes. In: International Conference on Boundary and Interior Layers (BAIL) - Computational and Asymptotic Methods.

Book Section

Houston, Paul (2017) Adjoint error estimation and adaptivity for hyperbolic problems. In: Handbook of Numerical Methods for Hyperbolic Problems. Applied and Modern Issues. Handbook of numerical analysis (18). Elsevier / North Holland, pp. 233-261. ISBN 9780444639103

Antonietti, Paola F., Cangiani, Andrea, Collis, Joe, Dong, Zhaonan, Georgoulis, Emmanuil H., Giani, Stefano and Houston, Paul (2015) Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. In: Lecture Notes in Computational Science and Engineering. Lecture Notes in Computational Science and Engineering . Springer Verlag. (Submitted)

Giani, Stefano and Houston, Paul (2010) High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. In: ADIGMA - a European initiative on the development of adaptive higher-order variational methods for aerospace applications. Notes on numerical fluid mechanics and multidisciplinary design (113). Springer, Berlin, pp. 399-411. ISBN 978-3-642-03706-1

Hartmann, Ralf and Houston, Paul (2009) Error estimation and adaptive mesh refinement for aerodynamic flows. In: Proceedings of the 36THCFD/Adigma course on HP-adaptive and HP-multigrid methods. von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium. ISBN 978-2-930389-98-2 (In Press)