Outputs (75)

Exponential Convergence of hp-ILGFEM for semilinear elliptic boundary value problems with monomial reaction (2025)
Journal Article
He, Y., Houston, P., Schwab, C., & Wihler, T. (in press). Exponential Convergence of hp-ILGFEM for semilinear elliptic boundary value problems with monomial reaction. IMA Journal of Numerical Analysis,

We study the fully explicit numerical approximation of a semilinear elliptic boundary value model problem, which features a monomial reaction and analytic forcing, in a bounded polygon Ω ⊂ R2 with a finite number of straight edges. In particular, we... Read More about Exponential Convergence of hp-ILGFEM for semilinear elliptic boundary value problems with monomial reaction.

Lubrication flow in grinding (2024)
Journal Article
Crowson, Z., Billingham, J., & Houston, P. (2024). Lubrication flow in grinding. Journal of Engineering Mathematics, 147(1), Article 12. https://doi.org/10.1007/s10665-024-10383-x

In the machining process known as grinding, fluid is applied to regulate the temperature of the workpiece and reduce the risk of expensive thermal damage. The factors that influence the transport of this grinding fluid are not well understood; howeve... Read More about Lubrication flow in grinding.

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport (2024)
Journal Article
Houston, P., Hubbard, M. E., Radley, T. J., Sutton, O. J., & Widdowson, R. S. J. (2024). Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport. Journal of Scientific Computing, 100(2), Article 52. https://doi.org/10.1007/s10915-024-02569-3

We introduce an hp–version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost... Read More about Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport.

Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation (2024)
Journal Article
Houston, P., Hubbard, M. E., & Radley, T. J. (2024). Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation. Computers and Mathematics with Applications, 166, 37-49. https://doi.org/10.1016/j.camwa.2024.04.011

In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a high-order/hp–version discontinuous Galerkin finite element approxi... Read More about Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation.

Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems (2024)
Journal Article
Radley, T. J., Houston, P., & Hubbard, M. E. (2024). Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems. Mathematics in Engineering, 6(1), 192-220. https://doi.org/10.3934/mine.2024009

In this article we consider the application of Euler’s homogeneous function theorem to- gether with Stokes’ theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two and three dimensio... Read More about Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems.

Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes (2022)
Journal Article
Congreve, S., & Houston, P. (2022). Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes. Advances in Computational Mathematics, 48(5), Article 54. https://doi.org/10.1007/s10444-022-09968-w

This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated poly... Read More about Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes.

Linearization of the Travel Time Functional in Porous Media Flows (2022)
Journal Article
Rourke, C. J., Houston, P., Rourke, C., & van der Zee, K. G. (2022). Linearization of the Travel Time Functional in Porous Media Flows. SIAM Journal on Scientific Computing, 44(3), B531-B557. https://doi.org/10.1137/21M1451105

The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the postclosure safety assessment of deep geological storage facilitie... Read More about Linearization of the Travel Time Functional in Porous Media Flows.

Gibbs phenomena for Lq-best approximation in finite element spaces (2022)
Journal Article
Houston, P., Roggendorf, S., & Van Der Zee, K. G. (2022). Gibbs phenomena for Lq-best approximation in finite element spaces. ESAIM: Mathematical Modelling and Numerical Analysis, 56(1), 177-211. https://doi.org/10.1051/m2an/2021086

Recent developments in the context of minimum residual finite element methods are paving the way for designing quasi-optimal discretization methods in non-standard function spaces, such as L q-type Sobolev spaces. For q → 1, these methods have demons... Read More about Gibbs phenomena for Lq-best approximation in finite element spaces.

High-Order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations (2021)
Book Chapter
Antonietti, P., Facciola, C., Houston, P., Mazzieri, I., Pennesi, G., & Verani, M. (2021). High-Order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations. In D. Di Pietro, L. Formaggia, & R. Masson (Eds.), Polyhedral methods in geosciences (159-225). Springer

An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids (2020)
Journal Article
Antonietti, P. F., Houston, P., Pennesi, G., & Suli, E. (2020). An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Mathematics of Computation, 89, 2047-2083. https://doi.org/10.1090/mcom/3510

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial diffe... Read More about An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids.