A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
Ridgway and Zhang, Shangyou
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
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math.NA 7years
2026 7verdicts
UNVERDICTED 7representative citing papers
Establishes L^p- and W^{1,p}-stability of the L2-projection on hybrid meshes for all K >= 2 in Q-RG and Q-RB refinements, extending prior results limited to parallelograms and K <= 9.
Bounded commuting projections for the 3D de Rham complex are built that preserve discrete polynomial traces and remain stable in a graph norm controlled by local oscillation near the boundary.
Derives reliable and efficient a posteriori error estimators for a general class of stabilized finite element methods applied to time-dependent mean field games, with an improved version for specific mass-lumping and affine-preserving stabilizations.
Develops pressure-robust LDG discretizations for the p-Stokes problem proving well-posedness, stability, and optimal or quasi-optimal error estimates for linear elements across p in (1,∞).
An exactly divergence-free Scott-Vogelius finite element scheme for the surface Stokes problem with inf-sup stability and optimal isoparametric convergence.
Optimal discretization error estimates are derived for conforming finite element solutions of the Stokes equations with approximated non-homogeneous Dirichlet boundary data, including very weak formulations for low-regularity cases.
citing papers explorer
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Numerical analysis of first-order mean field games under displacement monotonicity
A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
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Sobolev stability of the $L^2$-projection on hybrid meshes
Establishes L^p- and W^{1,p}-stability of the L2-projection on hybrid meshes for all K >= 2 in Q-RG and Q-RB refinements, extending prior results limited to parallelograms and K <= 9.
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Bounded, Commuting, Discrete-trace Preserving Projections
Bounded commuting projections for the 3D de Rham complex are built that preserve discrete polynomial traces and remain stable in a graph norm controlled by local oscillation near the boundary.
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A posteriori error bounds for finite element approximations of time-dependent mean field games
Derives reliable and efficient a posteriori error estimators for a general class of stabilized finite element methods applied to time-dependent mean field games, with an improved version for specific mass-lumping and affine-preserving stabilizations.
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Pressure-robust and quasioptimal Discontinuous Galerkin discretisations of the $p$-Stokes problem
Develops pressure-robust LDG discretizations for the p-Stokes problem proving well-posedness, stability, and optimal or quasi-optimal error estimates for linear elements across p in (1,∞).
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A Divergence-Free Scott-Vogelius Finite Element Method for the Surface Stokes Problem
An exactly divergence-free Scott-Vogelius finite element scheme for the surface Stokes problem with inf-sup stability and optimal isoparametric convergence.
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Numerical analysis for the Stokes problem with non-homogeneous Dirichlet boundary condition
Optimal discretization error estimates are derived for conforming finite element solutions of the Stokes equations with approximated non-homogeneous Dirichlet boundary data, including very weak formulations for low-regularity cases.