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 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.
Proves optimal-order a-priori error estimates for a linear BDF2 finite-element scheme applied to the LLG equation, establishing convergence to both weak and strong solutions under regularity assumptions.
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.
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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.