6 papers · 1 filter
Optimal control of a kinetic equation
Aaron Pim, Tristan Pryer, Alex Trenam
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-pos…
Cycle-Free Polytopal Mesh Sweeping for Boltzmann Transport
Ansar Calloo, Matthew Evans, Henry Lockyer +3
We introduce a novel property of bounded Voronoi tessellations that enables cycle-free mesh sweeping algorithms. We prove that a topological sort of the dual graph of any Voronoi t…
A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics…
Duality based error control for the Signorini problem
Ben S. Ashby, Tristan Pryer
In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates…
Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation
Ben S. Ashby, Tristan Pryer
In this article we present a numerical method for the Stokes flow of an Oldroyd-B fluid. The viscoelastic stress evolves according to a constitutive law formulated in terms of the…
A Nodally Bound-Preserving Finite Element Method
Gabriel Barrenechea, Emmanuil Georgoulis, Tristan Pryer +1
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator…