14 citations · 24 across the 7 of their papers we have counts for
9 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…
Learning from few examples with nonlinear feature maps
Ivan Y. Tyukin, Oliver Sutton, Alexander N. Gorban
In this work we consider the problem of data classification in post-classical settings were the number of training examples consists of mere few data points. We explore the phenome…
Residual-based a posteriori error estimates for -discontinuous Galerkin discretisations of the biharmonic problem
Zhaonan Dong, Lorenzo Mascotto, Oliver J. Sutton
We introduce a residual-based a posteriori error estimator for a novel -version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimen…
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
Andrea Cangiani, Emmanuil H. Georgoulis, Oliver J. Sutton
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very gene…
Long time a posteriori error estimates for fully discrete parabolic problems
Oliver J. Sutton
Computable estimates for the error of finite element discretisations of parabolic problems in the norm are developed, which exhibit constant effectivities (the…
Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework
Andrea Cangiani, Emmanuil H. Georgoulis, Andrew Yu. Morozov +1
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fas…
The Virtual Element Method in 50 lines of MATLAB
Oliver J. Sutton
We present a 50-line MATLAB implementation of the lowest order virtual element method for the two-dimensional Poisson problem on general polygonal meshes. The matrix formulation of…
A posteriori error estimates for the virtual element method
Andrea Cangiani, Emmanuil H. Georgoulis, Tristan Pryer +1
An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies o…
Conforming and nonconforming virtual element methods for elliptic problems
Andrea Cangiani, Gianmarco Manzini, Oliver J. Sutton
We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differe…