9 citations · 35 across the 11 of their papers we have counts for
13 papers
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Paul Houston, Matthew E. Hubbard, Thomas J. Radley +2
We introduce an -version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offeri…
Two-grid -version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes
Scott Congreve, Paul Houston
This article considers the extension of two-grid -version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic bou…
Linearisation of the Travel Time Functional in Porous Media Flows
Paul Houston, Connor J. Rourke, Kristoffer G. Van der Zee
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…
Gibbs Phenomena for -Best Approximation in Finite Element Spaces -- Some Examples
Paul Houston, Sarah Roggendorf, Kristoffer G. van der Zee
Recent developments in the context of minimum residual finite element methods are paving the way for designing finite element methods in non-standard function spaces. This, in part…
Eliminating Gibbs Phenomena: A Non-linear Petrov-Galerkin Method for the Convection-Diffusion-Reaction Equation
Paul Houston, Sarah Roggendorf, Kristoffer G. van der Zee
In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem i…
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
P. F. Antonietti, P. Houston, G. Pennesi +1
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 discont…
Automatic symbolic computation for discontinuous Galerkin finite element methods
Paul Houston, Nathan Sime
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, i…
Adaptive Refinement for -Version Trefftz Discontinuous Galerkin Methods for the Homogeneous Helmholtz Problem
Scott Congreve, Paul Houston, Ilaria Perugia
In this article we develop an -adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not…
An -Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems
Paul Houston, Thomas P. Wihler
In this paper we develop an -adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbat…
An Adaptive Variable Order Quadrature Strategy
Paul Houston, Thomas P. Wihler
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number o…
Adaptive Energy Minimisation for -Finite Element Methods
Paul Houston, Thomas P. Wihler
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…
Multigrid algorithms for -version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes
Paola F. Antonietti, Paul Houston, Xiaozhe Hu +2
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…
Enhancing SPH using moving least-squares and radial basis functions
R. A. Brownlee, P. Houston, J. Levesley +1
In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle app…