相关论文: A discrete variational scheme for isentropic proce…

The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…

In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…

In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…

The efficient manipulation of thermodynamic states within the finite time is fundamentally constrained by the intrinsic dissipative cost. While the slow-driving regime is well-characterized by a universal $1/\tau$-scaling of…

We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…

In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…

We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…

Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…

In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables…

Spinodal decomposition in a near-critical binary fluid is examined for experimental scenarios in which the liquid is quenched abruptly by changing the pressure and the subsequent phase separation occurs with no heat flow from the outside,…

In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…

Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…

Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…

We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently…

We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions…