Related papers: A time-splitting finite-element approximation for …
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…
New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
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…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…
We consider the vorticity formulation of the Euler equations describing the flow of a two-dimensional incompressible ideal fluid on the sphere. Zeitlin's model provides a finite-dimensional approximation of the vorticity formulation that…
We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < {\alpha} < 1. The stability properties…
In the present work, the Eulerian Large Eddy Simulation of dilute disperse phase flows is investigated. By highlighting the main advantages and drawbacks of the available approaches in the literature, a choice is made in terms of modelling:…
We consider the numerical approximation of a generalized fractional Oldroyd-B fluid problem involving two Riemann-Liouville fractional derivatives in time. We establish regularity results for the exact solution which play an important role…
We study the numerical solution of the quasi-static linear Biot's equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…