60 citations · 361 across the 27 of their papers we have counts for
27 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…
A posteriori error bounds for finite element approximations of steady-state mean field games
Yohance A. P. Osborne, Iain Smears, Harry Wells
We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the -n…
Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions
Yohance A. P. Osborne, Iain Smears
Mean field Game (MFG) Partial Differential Inclusions (PDI) are generalizations of the system of Partial Differential Equations (PDE) of Lasry and Lions to situations where players…
Near and full quasi-optimality of finite element approximations of stationary second-order mean field games
Yohance A. P. Osborne, Iain Smears
We establish a priori error bounds for monotone stabilized finite element discretizations of stationary second-order mean field games (MFG) on Lipschitz polytopal domains. Under su…
Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians
Yohance A. P. Osborne, Iain Smears
The standard formulation of the PDE system of Mean Field Games (MFG) requires the differentiability of the Hamiltonian. However in many cases, the structure of the underlying optim…
Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions
Yohance A. P. Osborne, Iain Smears
The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Pla…
Convergence of adaptive discontinuous Galerkin and -interior penalty finite element methods for Hamilton--Jacobi--Bellman and Isaacs equations
Ellya L. Kawecki, Iain Smears
We prove the convergence of adaptive discontinuous Galerkin and -interior penalty methods for fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs equati…
Unified analysis of discontinuous Galerkin and -interior penalty finite element methods for Hamilton--Jacobi--Bellman and Isaacs equations
Ellya L. Kawecki, Iain Smears
We provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and -IP finite element approximations of fully nonlinear se…
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal approximation estimates in
Alexandre Ern, Thirupathi Gudi, Iain Smears +1
Given an arbitrary function in H(div), we show that the error attained by the global-best approximation by H(div)-conforming piecewise polynomial Raviart-Thomas-Nédélec elements un…
Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems
Iain Smears, Martin Vohralík
We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrar…
Time-parallel iterative solvers for parabolic evolution equations
Martin Neumuller, Iain Smears
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint…
An adaptive -refinement strategy with computable guaranteed bound on the error reduction factor
Patrik Daniel, Alexandre Ern, Iain Smears +1
We propose a new practical adaptive refinement strategy for -finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-…
On the notion of boundary conditions in comparison principles for viscosity solutions
Max Jensen, Iain Smears
We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear…
Equilibrated flux a posteriori error estimates in -norms for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralik
We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming -finite element methods in space and an arbitrary order d…
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralík
We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high…
Discrete -robust -liftings and a posteriori estimates for elliptic problems with source terms
Alexandre Ern, Iain Smears, Martin Vohralík
We establish the existence of liftings into discrete subspaces of of piecewise polynomial data on locally refined simplicial partitions of polygonal/poly…
Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method
Iain Smears
The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system a…
Stable discontinuous Galerkin FEM without penalty parameters
Lorenz John, Michael Neilan, Iain Smears
We propose a modified local discontinuous Galerkin (LDG) method for second--order elliptic problems that does not require extrinsic penalization to ensure stability. Stability is i…
Nonoverlapping domain decomposition preconditioners for discontinuous Galerkin approximations of Hamilton--Jacobi--Bellman equations
Iain Smears
We analyse a class of nonoverlapping domain decomposition preconditioners for nonsymmetric linear systems arising from discontinuous Galerkin finite element approximation of fully…