相关论文: Adaptive Total Variation Stable Local Timestepping…

In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…

In this paper, the pressure correctionfinite element method is proposed for the 2D/3D time-dependent thermomicropolarfluid equations. Thefirst-order and second-order backward difference formulas (BDF) are adopted to approximate the time…

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…

This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…

This paper focuses on continuous data assimilation (CDA) for the Navier-Stokes equations with nonlinear slip boundary conditions. CDA methods are typically employed to recover the original system when initial data or viscosity coefficients…

We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…

The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…

This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the…

We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…

Recently, Galley [Phys. Rev. Lett. {\bf 110}, 174301 (2013)] proposed an initial value problem formulation of Hamilton's principle applied to non-conservative systems. Here, we explore this formulation for complex partial differential…

Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of…

When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…

Large-scale scientific simulations require significant resources to generate high-resolution time-varying data (TVD). While super-resolution is an efficient post-processing strategy to reduce costs, existing methods rely on a large amount…

A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact…

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be…

In this paper, we address the well-known challenge in the numerical solution of time-fractional partial differential equations (TFPDEs), namely, that the dependence on all previous time levels leads to storage requirements that grow…

Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang [{\em SIAM J. Imaging Sci.}, 1 (2008), pp. 248--272]. The method in a nutshell consists of a…

We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the $\mathcal{\tilde O}(t^{-1/4})$ rate of convergence for the norm of the gradient of…