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.
The Finite Element Method for Elliptic Problems
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A cP_n P_m scheme for DGSEM-LGL achieves m+1 convergence order via projected high-order components and a compact reconstruction operator that corrects the highest Legendre mode.
A linear BDF2 finite-element integrator for the LLG equation achieves first-order spatial and second-order temporal convergence rates and converges to both weak and strong solutions.
A Rocq formalization defines simplicial Lagrange finite elements as records with geometric data, polynomial approximations, and unisolvence proofs for any dimension and polynomial degree.
Mixed VEM with novel non-linear stabilization for p-Laplace equation, establishing non-Hilbertian inf-sup stability, continuity, coercivity, and a priori error estimates.
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
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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Projection-Based Reconstruction for Achieving High-Order Accuracy from Low-Order DGSEM Simulations
A cP_n P_m scheme for DGSEM-LGL achieves m+1 convergence order via projected high-order components and a compact reconstruction operator that corrects the highest Legendre mode.
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BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
A linear BDF2 finite-element integrator for the LLG equation achieves first-order spatial and second-order temporal convergence rates and converges to both weak and strong solutions.
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A Rocq Formalization of Simplicial Lagrange Finite Elements
A Rocq formalization defines simplicial Lagrange finite elements as records with geometric data, polynomial approximations, and unisolvence proofs for any dimension and polynomial degree.
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A Mixed Virtual Element Method for the p-Laplace equation
Mixed VEM with novel non-linear stabilization for p-Laplace equation, establishing non-Hilbertian inf-sup stability, continuity, coercivity, and a priori error estimates.
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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On a linear DG approximation of chemotaxis models with damping gradient nonlinearities
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.