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Related Articles from SNS

Numerical Approximation of the stochastic Cahn--Hilliard equation with singular potential

Announce Type: new Abstract: We discuss the numerical approximation of the stochastic Cahn--Hilliard equation with a singular double-obstacle potential and multiplicative conservative noise. We propose a regularised fully discrete finite element approximation scheme for the problem and show that it satisfies stability estimates which are uniform with respect to the discretization parameters. We show convergence of the approximation for vanishing discretization parameters towards a...

arXiv CS 2d ago

Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time

arXiv:2401.02878v5 Announce Type: replace-cross Abstract: Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense.

arXiv CS 1d ago

An explicit finite-memory scheme for approximating and sampling invariant measures of stochastic functional differential equations with infinite delay

arXiv:2603.04724v2 Announce Type: replace Abstract: Efficient sampling and numerical approximation of invariant probability measures (IPMs) on infinite-dimensional function spaces are important problems in scientific computing. In this paper, we study the numerical approximation and sampling of IPMs associated with stochastic functional differential equations with infinite delay (SFDEswID). To this end, we develop a fully explicit ergodicity-preserving truncated Euler--Maruyama scheme for...

arXiv CS 1d ago

Ferrofluids: Modeling and Approximation

Mathematics > Numerical Analysis [Submitted on 31 May 2026] Title:Ferrofluids: Modeling and Approximation View PDF HTML (experimental)Abstract:Starting from Maxwell's and linear momentum balance equations, we derive a ferrofluid model using the generalized Onsager's principle. Guided by a discrete perturbation estimate, we design and analyze families of Galerkin schemes that converge to sufficiently regular solutions and derive error estimates.

arXiv CS 8d ago

Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes

Announce Type: replace Abstract: We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings.

arXiv Physics 1d ago

Multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM). Theory and applications to upscaling of two-phase flow

arXiv:2606.01303v1 Announce Type: new Abstract: We develop a multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM) for constructing coarse-scale models in heterogeneous media that simultaneously provide accurate numerical approximations and physically consistent macroscopic equations. Classical multiscale methods efficiently approximate fine-scale solutions on coarse grids using localized basis functions, but they do not offer a systematic pathway for deriving macroscopic...

arXiv CS 8d ago

Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators

Announce Type: replace Abstract: Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and efficient evaluation...

arXiv CS 5d ago

A Measure-Consistent Operator Learning Method for Infinite-Dimensional Master Equations

Announce Type: new Abstract: Master equations in mean field game theory characterize feedback value functions that depend on time, state (space), and the population distribution. Their numerical approximation is challenging because the unknown is defined on a space of probability measures and the equation involves intrinsic measure derivatives and nonlocal population terms. This paper proposes a measure-consistent operator learning method (MCOL) for infinite-dimensional master equations.

arXiv CS 1d ago

Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators

arXiv:2402.02247v3 Announce Type: replace Abstract: Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and...

arXiv CS 8d ago

A Variational Framework for the Complexity of PDE Solutions

arXiv:2510.21290v3 Announce Type: replace Abstract: Partial Differential Equations (PDEs) are fundamental mathematical models for describing physical phenomena, yet most PDEs of practical interest require numerical approximations. The feasibility of such methods is constrained by existing computational models. Since digital computers are the primary realizations of numerical computations, and Turing machines define their theoretical limits, computability of PDE solutions is of fundamental...

arXiv CS 1d ago