相关论文: A symmetrized parametric finite element method for…

In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…

We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in…

Diffusion problems with anisotropic features arise in the various areas of science and engineering fields. As a Lagrangian mesh-less method, SPH has a special advantage in addressing the diffusion problems due to the the benefit of dealing…

In this paper, we propose two low order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the non-conforming FEM of Kouhia and Stenberg (1995, Comput. Methods Appl. Mech. Engrg.). The finite…

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…

This work develops a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two dimensional continua. The method employs Wachspress rational basis functions to construct conforming…

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…

This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discussed. Differential operators are represented by sparse…

We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…

Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…

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…

This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…

We propose and analyze a semi-discrete parametric finite element scheme for solving the area-preserving curve shortening flow. The scheme is based on Dziuk's approach (SIAM J. Numer. Anal. 36(6): 1808-1830, 1999) for the anisotropic curve…

In this manuscript, we present a mixed finite element discretization for a class of boundary-damped anisotropic port-Hamiltonian systems. Using a multiplier method, we demonstrate that the resulting approximation model uniformly preserves…

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…