Abstract. Based on a validated two-dimensional XFEM code for two-phase flows, this work deals with the extension of this code to three spatial dimensions using structured hexahedral meshes. Surface tension effects are considered, resulting in a discontinuous pressure field. The treatment of hexahedral elements which are cut by the interface is shown. In contrast to linear tetrahedral elements, ...

This paper is concerned with residual type a posteriori error estimators for finite element methods for the Stokes equations. In particular, the authors established a unified approach for deriving and analyzing a posteriori error estimators for velocity-pressure based finite element formulations for the Stokes equations. A general a posteriori error estimator was presented with a unified mathem...

This work is concerned with the discontinuous Galerkin finite approximations for the steady Stokes equations driven by slip boundary condition of “friction” type. Assuming that the flow region is a bounded, convex domain with a regular boundary, we formulate the problem and its discontinuous Galerkin approximations as mixed variational inequalities of the second kind with primitive variables. T...

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature T_{m} happening at a crossover density ρ_{m}. Th...

A series of efforts were made to solve a simple ablation problem with gas motion through the porous media employing finite element based Galerkin and Discontinuous Galerkin methods. First, one-dimensional solutions of Euler and magneto-hydrodynamics (MHD) equations are presented for comparison with analytical results, to validate the code. The spurious oscillations of standard Galerkin approach...

A numerical method for the simulation of three-dimensional incompressible twophase flows is presented. The proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two-phase flow problems with a level set method implemented with a quadrature-free Discontinuous Galerkin (DG) method [1]. The use of a fast contouring algorithm [2] permits...

A discretization scheme applicable to the direct approximation of the velocity variable for either a rst-order system or second-order elliptic equation is proposed in this paper. The scheme is motivated by mixed nite element methods and extends the cell-centered nite diierence and the nite volume element methods to problems with discontinuous coeecients and various boundary conditions. Error es...

Accurate simulation of flow behaviors in fractured porous media is challenging. We present a discontinuous Galerkin (DG) approximation and continuous (CG) for compressible single- two-phase with conducting (high permeable) blocking (low fractures using mixed-dimensional approach which the fracture described as reduced-dimensional interface coupled linear transmission conditions. The proposed DG...

We report on the pressure-induced phase transition in a model of paracrystalline silicon ~amorphous silicon with a crystalline grain! using an ab initio constant pressure simulation technique. The paracrystalline model transforms into a high-density amorphous phase at 16 GPa with a discontinuous volume change of ;24%. The transformation of the crystalline grain begins at the boundary and procee...

In this paper, two postprocessing procedures for pressure recovery are proposed and analyzed for the weakly over-penalized discontinuous Galerkin methods developed in Liu in SIAM J Numer Anal 49:2165–2181, 2011 for the Stokes problem in two dimensions. These pressure recovery procedures are just elementwise calculations, benefiting from the weak over-penalization in the corresponding velocity s...