相关论文: Mixed finite elements for convection-coupled phase…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
This article discusses computational techniques for simulating natural convection in three-dimensional domains using finite element methods with tetrahedral elements. These techniques form a new numerical procedure for this kind of…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the…
Our previous molecular dynamic simulation studies of simple two-dimensional (2D) systems \cite{matt_big} suggested that both geometrical defects (localized, large-amplitude deviations from hexagonal ordering) and topological defects…
For the calculation of complex neutral/ionized gas phase chemical equilibria, we present a semi-analytical versatile and efficient computer program, called FastChem. The applied method is based on the solution of a system of coupled…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection of active…
This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software package COMSOL Multiphysics for multi-field thermo-hydro-mechanical problems in discontinuous porous media. To…
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…
The simulation of rare events is one of the key problems in atomistic simulations. Towards its solution a plethora of methods have been proposed. Here we combine two such methods metadynamics and inte-grated tempering sampling. In…
We present the technical details of an experimental method to realize a model system for 2D phase transitions and the glass transition. The system consists of several hundred thousand colloidal super-paramagnetic particles confined by…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
We present a robust numerical method for solving incompressible, immiscible two-phase flows. The method extends the monolithic phase conservative level set method with embedded redistancing by Quezada de Luna et al. [38] and a semi-implicit…
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal…
Structural materials are broadly used in applications such as nuclear vessels, high-temperature processes, and civil construction. Usually, during their placing and lifespan, they may present free or chemically bonded liquid phases in their…