相关论文: A linear, unconditionally stable, second order dec…

The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter Q for the orientational order is coupled with a real scalar…

We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear…

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous…

In this paper we propose and analyze a second order accurate (in time) numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in…

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…

We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-reformulated system the original nonlinear term is replaced by a…

In this paper, we investigate linear first- and second-order numerical schemes for the Allen--Cahn equation with a general (possibly degenerate) mobility. Compared with existing numerical methods, our schemes employ a novel dynamic…

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…

We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…

We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…

We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy…

We construct efficient original-energy-dissipative schemes for the Navier-Stokes-Darcy model and related two-phase flows using a prediction-correction framework. A new relaxation technique is incorporated in the correction step to guarantee…

We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equations. The viscous terms are treated by a standard perturbative…

In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins…

The Ericksen-Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows of nematic type. In this paper, we prove the uniqueness of global weak solutions to the general…

We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…

The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reduced…

This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…

An adaptive implicit-explicit (IMEX) BDF2 scheme is investigated on generalized SAV approach for the Cahn-Hilliard equation by combining with Fourier spectral method in space. It is proved that the modified energy dissipation law is…