相关论文: Convergence Analysis for a Finite Element Approxim…
In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…
In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schr\"{o}dinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To…
To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
The numerical implementation of finite element discretization method for the stream function formulation of a linearized Navier-Stokes equations is considered. Algorithm 1 is applied using Argyris element. Three global orderings of nodes…
In this research, we introduce and investigate an approximation method that preserves the structural integrity of the non-isothermal Cahn-Hilliard-Navier-Stokes system. Our approach extends a previously proposed technique [1], which…
This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…
In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…
We present and analyze a fully discrete fractional time stepping technique for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material…
In the present paper, we propose a Local Discontinuous Galerkin (LDG) approximation for fully non-homogeneous systems of $p$-Navier-Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Navier-Stokes equations corresponding to given measurements on…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
This work presents a finite element method for a modified Poisson-Nernst-Planck/Navier-Stokes (PNP/NS) model under the mechanical equilibrium, developed for compressible electrolytes. Another key contribution of this work is the reduction…
Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…