Related papers: A Two-level Finite Element Method for Viscoelastic…
Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci.…
Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by…
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation…
Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate…
In this paper, we derive optimal L2- and H1-norm error estimates for a fully discrete convex-splitting decoupled finite element method (FEM) for the two-phase diffuse interface magnetohydrodynamics (MHD) system. We use the semi-implicit…
We consider a stabilized finite element method for the Darcy problem on a surface based on the Masud-Hughes formulation. A special feature of the method is that the tangential condition of the velocity field is weakly enforced through the…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
In this article we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a…
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…
In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and a Hessian recovery based linear (HRBL) FEM for second order elliptic equations in non-divergence form. The elliptic equation is casted into a…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
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 develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…