5 papers
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…
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…
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…