15 citations · 33 across the 9 of their papers we have counts for
10 papers
Efficient Proton Transport Modelling for Proton Beam Therapy and Biological Quantification
Ben S. Ashby, Veronika Chronholm, Daniel K. Hajnal +4
In this work, we present a fundamental mathematical model for proton transport, tailored to capture the key physical processes underpinning Proton Beam Therapy (PBT). The model pro…
A Bayesian Inverse Approach to Proton Therapy Dose Delivery Verification
Alexander M. G. Cox, Laura Hattam, Andreas E. Kyprianou +1
This study presents a proof-of-concept for a novel Bayesian inverse method in a one-dimensional setting, aimed at proton beam therapy treatment verification. Our methodology is pre…
Residual estimates for post-processors in elliptic problems
Andreas Dedner, Jan Giesselmann, Tristan Pryer +1
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `twe…
On the numerical approximation of vectorial absolute minimisers in
Nikos Katzourakis, Tristan Pryer
Let be an open set. We consider the supremal functional \[ \tag{1} \label{1} \ \ \ \ \ \ \mathrm{E}_\infty (u,\mathcal{O})\, :=\, \| \mathrm D u \|_{L^\infty( \mathcal{O} )}, \…
The design of conservative finite element discretisations for the vectorial modified KdV equation
James Jackaman, Georgios Papamikos, Tristan Pryer
We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation. We demonstrate that the scheme conserves energy up to machine pre…
A Symmetry Analysis of the -Polylaplacian
Georgios Papamikos, Tristan Pryer
In this work we use Lie group theoretic methods and the theory of prolonged group actions to study two fully nonlinear partial differential equations (PDEs). First we consider a th…
On the numerical approximation of -Biharmonic and -Biharmonic functions
Nikos Katzourakis, Tristan Pryer
In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in . The associated equation, coined the -Bilaplacian, is a \emph{third o…
Second Order Variational Problems and the -Polylaplacian
Nikos Katzourakis, Tristan Pryer
In this paper we initiate the study of nd order variational problems in , seeking to minimise the norm of a function of the hessian. We also derive and stud…
On the Numerical Approximation of -Harmonic Mappings
Nikos Katzourakis, Tristan Pryer
Given a map , the -Laplacian is the system \[ \label{1} Δ_\infty u \, :=\, \Big(\text{D}u \otimes \text{D}u + |\te…
A review from the PDE viewpoint of Hamilton-Jacobi-Bellman Equations Arising in Optimal Control with Vectorial Cost
Nikos Katzourakis, Tristan Pryer
This paper is a review of results on Optimisation which are perhaps not so standard in the PDE realm. To this end, we consider the problem of deriving the PDEs associated to the op…