相关论文: Finite element approximation to the non-stationary…

This paper presents a conforming finite element semi-discretization of the streamfunction form of the one-layer unsteady quasi-geostrophic equations, which are a commonly used model for large-scale wind-driven ocean circulation. We derive…

This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation.…

We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…

In this paper we proposed a two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation. Optimal error estimates for the two-level finite element…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

We propose some finite element schemes to solve a class of fourth-order nonlinear PDEs, which include the vector-valued Landau--Lifshitz--Baryakhtar equation, the Swift--Hohenberg equation, and various Cahn--Hilliard-type equations with…

We extend the DeTurck trick from the classical isotropic curve shortening flow to the anisotropic setting. Here the anisotropic energy density is allowed to depend on space, which allows an interpretation in the context of Finsler metrics,…

This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

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…

This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere equation and a transport equation. The system is the Eulerian formulation in the dual…

We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…

This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…

In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that…

We present a continuous and a discontinuous linear Finite Element method based on a predictor-corrector scheme for the numerical approximation of the Ericksen-Leslie equations, a model for nematic liquid crystal flow including a non-convex…

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward…

We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…