SUMMARY A study of spurious currents in continuous finite element based simulations the incompressible Navier–Stokes equations for two‐phase flows is presented on basis computations a circular drop equilibrium. The conservative and standard level set methods are used. It shown that sharp surface tension force, expressed as line integral along interface, can give rise to large oscillations pressure do not decrease with mesh refinement. If instead regularized representation used, exact force...

In the present study, response surface methodology was employed to investigate effects of main variables, including initial MB concentration, hydrogen peroxide dosage, current density, and electrolysis time on removal efficiency using electro-Fenton (EF) process. The concentration determination by UV-VIS spectrometer. EF process degrades contaminant molecules highly oxidizing species •OH. A quadratic regression model developed predict MB, where R2 value found be 0.9970, which indicates...

Abstract We develop and analyse a stabilization term for cut finite element approximations of an elliptic second-order partial differential equation on surface embedded in ${\mathbb{R}}^d$. The new combines properly scaled normal derivatives at the together with control jump across faces, provides variation solution active three-dimensional elements that intersect surface. show condition number stiffness matrix is $O(h^{-2})$, where $h$ mesh parameter. works linear as well higher-order...

We propose a new unfitted finite element method for simulation of two-phase flows in presence insoluble surfactant. The key features the are 1) discrete conservation surfactant mass; 2) possibility having meshes that do not conform to evolving interface separating immiscible fluids; 3) accurate approximation quantities with weak or strong discontinuities across geometries such as velocity field and pressure. discretization incompressible Navier-Stokes equations coupled convection-diffusion...

We develop a stabilized cut finite element method for the convection problem on surface based continuous piecewise linear approximation and gradient jump stabilization terms. The discrete cuts through background mesh consisting of tetrahedra in an arbitrary way space consists functions defined mesh. variational form involves integrals term is full faces tetrahedra. serves two purposes: first secondly resulting system equations algebraically stable. establish stability results that are...

The mean curvature vector of a surface is obtained by letting the Laplace--Beltrami operator act on embedding in ${\bf R}^3$. In this contribution we develop stabilized finite element approximation certain piecewise linear surfaces which enjoys first order convergence $L^2$. stabilization involves jump tangent gradient direction outer co-normals at each edge mesh. We consider both standard meshed and so-called cut that are level sets distance functions. prove priori error estimates verify...

In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The are based on the discontinuous Galerkin framework and use regular background mesh, where interior boundaries allowed to through mesh arbitrarily. Our include ghost penalty stabilization handle small elements new reconstruction approximation macro-elements, which local patches consisting un-cut neighboring that connected by...

Abstract We develop two unfitted finite element methods for the Stokes equations based on $$\textbf{H}^{{{\,\textrm{div}\,}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mspace/> <mml:mtext>div</mml:mtext> </mml:mrow> </mml:msup> </mml:math> -conforming elements. Both cut exhibit optimal convergence order velocity, pointwise divergence-free velocity fields, and well-posed linear systems, independently of position boundary relative...

Density matrix purification, is in this work, used to facilitate the computation of eigenpairs around highest occupied and lowest unoccupied molecular orbitals (HOMO LUMO, respectively) electronic structure calculations. The ability purification give large separation between eigenvalues close HOMO-LUMO gap accelerate convergence Lanczos method. Illustrations indicate that a new eigenpair found more often than every second iteration when proposed methods are used.

We develop a conservative cut finite element method for an elliptic coupled bulk-interface problem. The is based on discontinuous Galerkin framework where stabilization added in such way that we retain conservation macroelements containing one with large intersection the domain and possibly number of elements small intersections. derive error estimates present confirming numerical results.