Paul Houston
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View article: Exponential convergence of <i>hp</i>-ILGFEM for semilinear elliptic boundary value problems with monomial reaction
Exponential convergence of <i>hp</i>-ILGFEM for semilinear elliptic boundary value problems with monomial reaction Open
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 $\varOmega \subset{\mathbb{R}}^{2}$ with a finite numb…
View article: Gradient Flow Finite Element Discretisations with Energy-Based $hp$-Adaptivity for the Gross-Pitaevskii Equation with Angular Momentum
Gradient Flow Finite Element Discretisations with Energy-Based $hp$-Adaptivity for the Gross-Pitaevskii Equation with Angular Momentum Open
This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects such as Bose-Einstein condensates (BECs). In this regime, …
View article: The effects of maternal flow on placental diffusion‐weighted <scp>MRI</scp> and intravoxel incoherent motion parameters
The effects of maternal flow on placental diffusion‐weighted <span>MRI</span> and intravoxel incoherent motion parameters Open
Purpose To investigate and explain observed features of the placental DWI signal in healthy and compromised pregnancies using a mathematical model of maternal blood flow. Methods Thirteen healthy and nine compromised third trimester pregna…
View article: Lubrication flow in grinding
Lubrication flow in grinding Open
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 underst…
View article: Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport Open
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 …
View article: Exponential Convergence of $hp$-ILGFEM for semilinear elliptic boundary value problems with monomial reaction
Exponential Convergence of $hp$-ILGFEM for semilinear elliptic boundary value problems with monomial reaction Open
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 $Ω\subset\mathbb{R}^2$ with a finite number of straigh…
View article: Quadrature-free polytopic discontinuous Galerkin methods for transport problems
Quadrature-free polytopic discontinuous Galerkin methods for transport problems Open
In this article we consider the application of Euler's homogeneous function theorem together with Stokes' theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two and three…
View article: Analysis of Iterative Methods for the Linear Boltzmann Transport Equation
Analysis of Iterative Methods for the Linear Boltzmann Transport Equation Open
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 discontinuous Galerkin finite element approximation in s…
View article: Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems
Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems Open
In this article we consider the application of Euler's homogeneous function theorem together with Stokes' theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two- and thre…
View article: A divergence free $C^0$-RIPG stream function formulation of the incompressible Stokes system with variable viscosity
A divergence free $C^0$-RIPG stream function formulation of the incompressible Stokes system with variable viscosity Open
Pointwise divergence free velocity field approximations of the Stokes system are gaining popularity due to their necessity in precise modelling of physical flow phenomena. Several methods have been designed to satisfy this requirement; how…
View article: Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport Open
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…
View article: Linearization of the Travel Time Functional in Porous Media Flows
Linearization of the Travel Time Functional in Porous Media Flows Open
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 storag…
View article: Gibbs phenomena for L<i><sup>q</sup></i>-best approximation in finite element spaces
Gibbs phenomena for L<i><sup>q</sup></i>-best approximation in finite element spaces Open
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 q -type Sobolev spaces. For q → 1, these methods h…
View article: Two-grid $hp$-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes
Two-grid $hp$-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes Open
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 aggl…
View article: Linearisation of the Travel Time Functional in Porous Media Flows
Linearisation of the Travel Time Functional in Porous Media Flows Open
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 post-closure safety assessment of deep geological stora…
View article: An hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems
An hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems Open
In this article we consider the a posteriori error analysis of hp -version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of strongly monotone type. In…
View article: An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids Open
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 p…
View article: Two‐Grid <i>hp</i>‐DGFEMs on Agglomerated Coarse Meshes
Two‐Grid <i>hp</i>‐DGFEMs on Agglomerated Coarse Meshes Open
We generalise the a priori error analysis of two‐grid hp ‐version discontinuous Galerkin finite element methods for strongly monotone second‐order quasilinear elliptic partial differential equations to the case when coarse meshes consistin…
View article: Gibbs Phenomena for $L^q$-Best Approximation in Finite Element Spaces -- Some Examples
Gibbs Phenomena for $L^q$-Best Approximation in Finite Element Spaces -- Some Examples Open
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 particular, permits the selection of a solution space in which …
View article: The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method
The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method Open
While it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space H 0 1 ( Ω ) {H_{0}^{1}(\Omega)} , the Banach Sobolev space W 0 1 , q ( Ω ) {W^{1,q}_{0}(\Omega)} , 1 …
View article: An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems Open
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and…
View article: An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids Open
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 pa…
View article: Output feedback control of flow separation over an aerofoil using plasma actuators
Output feedback control of flow separation over an aerofoil using plasma actuators Open
We address the problem of controlling the unsteady flow separation over an aerofoil, using plasma actuators. Despite the complexity of the dynamics of interest, we show how the problem of controlling flow separation can be formulated as a …