10 papers
The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations
Thomas Hall, Iain Smears, Endre Süli +1
Modern finite element libraries allow users to express partial differential equations directly in variational form, with the added convenience of automatic quadrature selection. In…
A posteriori error bounds for finite element approximations of time-dependent mean field games
Iain Smears, Harry Wells
We present a posteriori error bounds for a general class of stabilized finite element approximations of time-dependent mean field games. We first show the equivalence between the n…
Fully nonlinear second-order mean field games with nondifferentiable Hamiltonians
Thomas Sales, Iain Smears
We analyse fully nonlinear second-order mean field games (MFG) with nondifferentiable Hamiltonians, which take the form of a coupled system of a fully nonlinear Hamilton-Jacobi-Bel…
An introduction to the a posteriori error analysis of parabolic partial differential equations
Iain Smears
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of ste…
On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm
Iain Smears
For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori…
Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians
Yohance A. P. Osborne, Iain Smears
We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal…