Related papers: Mean conservation for density estimation via diffu…
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We propose an implementation of linear finite element method for nonlocal diffusion problem in 2D space. In the implementation, we reduce the integral from 4D to 2D which would simplify the computation significantly.
We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
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…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…